{"id":40875,"date":"2025-05-30T12:26:20","date_gmt":"2025-05-30T04:26:20","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/40875.html"},"modified":"2025-05-30T12:26:20","modified_gmt":"2025-05-30T04:26:20","slug":"%e5%9f%ba%e4%ba%8epiecewise-jerk-speed-optimizer%e7%9a%84%e9%80%9f%e5%ba%a6%e8%a7%84%e5%88%92%e7%ae%97%e6%b3%95%e9%99%84ros-c-python%e4%bb%bf%e7%9c%9f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/40875.html","title":{"rendered":"\u57fa\u4e8ePiecewise Jerk Speed Optimizer\u7684\u901f\u5ea6\u89c4\u5212\u7b97\u6cd5(\u9644ROS C++\/Python\u4eff\u771f)"},"content":{"rendered":"<\/p>\n<h4>\u76ee\u5f55<\/h4>\n<ul>\n<li>1 \u65f6\u7a7a\u89e3\u8026\u8fd0\u52a8\u89c4\u5212<\/li>\n<li>2 PJSO\u901f\u5ea6\u89c4\u5212\u539f\u7406<\/li>\n<li>\n<ul>\n<li>2.1 \u4f18\u5316\u53d8\u91cf<\/li>\n<li>2.2 \u4ee3\u4ef7\u51fd\u6570<\/li>\n<li>2.3 \u7ea6\u675f\u6761\u4ef6<\/li>\n<li>2.4 \u4e8c\u6b21\u89c4\u5212\u5f62\u5f0f<\/li>\n<\/ul>\n<\/li>\n<li>3 \u7b97\u6cd5\u4eff\u771f<\/li>\n<li>\n<ul>\n<li>3.1 ROS C&#043;&#043;\u4eff\u771f<\/li>\n<li>3.2 Python\u4eff\u771f<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>1 \u65f6\u7a7a\u89e3\u8026\u8fd0\u52a8\u89c4\u5212<\/h2>\n<p>\u5728\u81ea\u4e3b\u79fb\u52a8\u7cfb\u7edf\u7684\u8fd0\u52a8\u89c4\u5212\u4f53\u7cfb\u4e2d&#xff0c;<font color=\"#4a86e8\">\u65f6\u7a7a\u89e3\u8026<\/font>\u7684\u9012\u8fdb\u5f0f\u67b6\u6784\u56e0\u5176\u9ad8\u6548\u6027\u4e0e\u5de5\u7a0b\u53ef\u5b9e\u73b0\u6027\u88ab\u5e7f\u6cdb\u91c7\u7528\u3002\u8fd9\u4e00\u67b6\u6784\u5c06\u590d\u6742\u7684\u9ad8\u7ef4\u8fd0\u52a8\u89c4\u5212\u95ee\u9898\u5206\u89e3\u4e3a\u8def\u5f84\u89c4\u5212\u4e0e\u901f\u5ea6\u89c4\u5212\u4e24\u4e2a\u5c42\u6b21\u5316\u9636\u6bb5&#xff1a;\u8def\u5f84\u89c4\u5212\u9636\u6bb5\u57fa\u4e8e\u9759\u6001\u73af\u5883\u7ea6\u675f\u751f\u6210\u65e0\u78b0\u649e\u7684\u51e0\u4f55\u8f68\u8ff9&#xff1b;\u901f\u5ea6\u89c4\u5212\u9636\u6bb5\u5219\u5728\u6b64\u57fa\u7840\u4e0a\u5f15\u5165\u65f6\u95f4\u7ef4\u5ea6&#xff0c;\u901a\u8fc7\u52a8\u6001\u969c\u788d\u7269\u9884\u6d4b\u3001\u8fd0\u52a8\u5b66\u7ea6\u675f\u5efa\u6a21\u7b49\u4e3a\u673a\u5668\u4eba\u6216\u8f66\u8f86\u8d4b\u4e88\u65f6\u95f4\u8f74\u4e0a\u7684\u8fd0\u52a8\u89c4\u5f8b\u3002\u8fd9\u79cd\u89e3\u8026\u7b56\u7565\u867d\u5728\u7406\u8bba\u4e0a\u727a\u7272\u4e86\u65f6\u7a7a\u8054\u5408\u4f18\u5316\u7684\u6700\u4f18\u6027&#xff0c;\u5374\u901a\u8fc7\u5206\u5c42\u964d\u7ef4\u5927\u5e45\u63d0\u5347\u4e86\u590d\u6742\u573a\u666f\u4e0b\u7684\u8ba1\u7b97\u6548\u7387&#xff0c;\u4f7f\u5176\u6210\u4e3a\u81ea\u52a8\u9a7e\u9a76\u3001\u670d\u52a1\u673a\u5668\u4eba\u7b49\u5b9e\u65f6\u7cfb\u7edf\u7684\u7ecf\u5178\u65b9\u6848\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/05\/20250530042618-6839336ac9f52.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"650\" \/><\/p>\n<h2>2 PJSO\u901f\u5ea6\u89c4\u5212\u539f\u7406<\/h2>\n<h3>2.1 \u4f18\u5316\u53d8\u91cf<\/h3>\n<p><font color=\"#4a86e8\">\u5206\u6bb5\u52a0\u52a0\u901f\u5ea6\u4f18\u5316(Piecewise Jerk Speed Optimizer, PJSO)<\/font>\u7b97\u6cd5\u662f\u5e38\u7528\u7684\u7eb5\u5411\u901f\u5ea6\u4f18\u5316\u65b9\u5f0f&#xff0c;\u6838\u5fc3\u539f\u7406\u662f\u7528\u4e09\u6b21\u591a\u9879\u5f0f\u8868\u793as-t\u56fe\u4e2d\u6bcf\u4e2a\u65f6\u95f4\u533a\u95f4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         [ <\/p>\n<p>          t <\/p>\n<p>          k <\/p>\n<p>         , <\/p>\n<p>          t <\/p>\n<p>           k <\/p>\n<p>           &#043; <\/p>\n<p>           1 <\/p>\n<p>         ) <\/p>\n<p>        \\\\left[ t_k,t_{k&#043;1} \\\\right) <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">[<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em\">k<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u901f\u5ea6\u66f2\u7ebf&#xff0c;\u5e76\u7ea6\u675f\u6bcf\u4e2a\u533a\u95f4\u52a0\u52a0\u901f\u5ea6\u76f8\u7b49&#xff0c;\u5176\u4e2d<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         k <\/p>\n<p>         &#061; <\/p>\n<p>         0 <\/p>\n<p>         , <\/p>\n<p>         1 <\/p>\n<p>         , <\/p>\n<p>         \u22ef<br \/>\n       \u2009 <\/p>\n<p>         , <\/p>\n<p>         n <\/p>\n<p>         \u2212 <\/p>\n<p>         2 <\/p>\n<p>        k&#061;0,1,\\\\cdots ,n-2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em;vertical-align: 0em\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83888em;vertical-align: -0.19444em\"><\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em;vertical-align: 0em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c; \u53ef\u53d6\u4e3a\u8def\u5f84\u89c4\u5212\u7684\u8def\u70b9\u6570\u91cf\u3002PJSO\u7b97\u6cd5\u7684\u4f18\u5316\u53d8\u91cf\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          x <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 l <\/p>\n<p>                  s <\/p>\n<p>                  0 <\/p>\n<p>                  s <\/p>\n<p>                  \u02d9 <\/p>\n<p>                 0 <\/p>\n<p>                  s <\/p>\n<p>                  \u00a8 <\/p>\n<p>                 0 <\/p>\n<p>                \u22ef <\/p>\n<p>                 s <\/p>\n<p>                 k <\/p>\n<p>                  s <\/p>\n<p>                  \u02d9 <\/p>\n<p>                 k <\/p>\n<p>                  s <\/p>\n<p>                  \u00a8 <\/p>\n<p>                 k <\/p>\n<p>                \u22ef <\/p>\n<p>                 s <\/p>\n<p>                  n <\/p>\n<p>                  \u2212 <\/p>\n<p>                  1 <\/p>\n<p>                  s <\/p>\n<p>                  \u02d9 <\/p>\n<p>                  n <\/p>\n<p>                  \u2212 <\/p>\n<p>                  1 <\/p>\n<p>                  s <\/p>\n<p>                  \u00a8 <\/p>\n<p>                  n <\/p>\n<p>                  \u2212 <\/p>\n<p>                  1 <\/p>\n<p>            ] <\/p>\n<p>            3 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            1 <\/p>\n<p>           T <\/p>\n<p>         \\\\boldsymbol{x}&#061;\\\\left[ \\\\begin{matrix}{l} s_0&amp; \\\\dot{s}_0&amp; \\\\ddot{s}_0&amp; \\\\cdots&amp; s_k&amp; \\\\dot{s}_k&amp; \\\\ddot{s}_k&amp; \\\\cdots&amp; s_{n-1}&amp; \\\\dot{s}_{n-1}&amp; \\\\ddot{s}_{n-1}\\\\\\\\\\\\end{matrix} \\\\right] _{3n\\\\times 1}^{T} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.44444em;vertical-align: 0em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.53927em;vertical-align: -0.458041em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em\">l<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"minner\">\u22ef<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"minner\">\u22ef<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.85em\"><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.35em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">]<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.08123em\"><span class=\"\" style=\"top: -2.30029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.3029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em\">T<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.458041em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>2.2 \u4ee3\u4ef7\u51fd\u6570<\/h3>\n<p>\u4ee3\u4ef7\u51fd\u6570\u53ef\u8bbe\u8ba1\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          J <\/p>\n<p>          &#061; <\/p>\n<p>           \u2211 <\/p>\n<p>            i <\/p>\n<p>            &#061; <\/p>\n<p>            0 <\/p>\n<p>            n <\/p>\n<p>            \u2212 <\/p>\n<p>            2 <\/p>\n<p>           ( <\/p>\n<p>            w <\/p>\n<p>            s <\/p>\n<p>             ( <\/p>\n<p>              s <\/p>\n<p>              i <\/p>\n<p>             \u2212 <\/p>\n<p>              s <\/p>\n<p>               i <\/p>\n<p>               , <\/p>\n<p>                r <\/p>\n<p>                e <\/p>\n<p>                f <\/p>\n<p>             ) <\/p>\n<p>            2 <\/p>\n<p>           &#043; <\/p>\n<p>            w <\/p>\n<p>            v <\/p>\n<p>             ( <\/p>\n<p>               s <\/p>\n<p>               \u02d9 <\/p>\n<p>              i <\/p>\n<p>             \u2212 <\/p>\n<p>               s <\/p>\n<p>               \u02d9 <\/p>\n<p>               i <\/p>\n<p>               , <\/p>\n<p>                r <\/p>\n<p>                e <\/p>\n<p>                f <\/p>\n<p>             ) <\/p>\n<p>            2 <\/p>\n<p>           &#043; <\/p>\n<p>            w <\/p>\n<p>            a <\/p>\n<p>             s <\/p>\n<p>             \u00a8 <\/p>\n<p>            i <\/p>\n<p>            2 <\/p>\n<p>           &#043; <\/p>\n<p>            w <\/p>\n<p>            j <\/p>\n<p>            s <\/p>\n<p>            i <\/p>\n<p>             ( <\/p>\n<p>             3 <\/p>\n<p>             ) <\/p>\n<p>             2 <\/p>\n<p>           ) <\/p>\n<p>          &#043; <\/p>\n<p>           w <\/p>\n<p>            s <\/p>\n<p>            , <\/p>\n<p>             e <\/p>\n<p>             n <\/p>\n<p>             d <\/p>\n<p>            ( <\/p>\n<p>             s <\/p>\n<p>              n <\/p>\n<p>              \u2212 <\/p>\n<p>              1 <\/p>\n<p>            \u2212 <\/p>\n<p>             s <\/p>\n<p>              e <\/p>\n<p>              n <\/p>\n<p>              d <\/p>\n<p>            ) <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>           w <\/p>\n<p>            v <\/p>\n<p>            , <\/p>\n<p>             e <\/p>\n<p>             n <\/p>\n<p>             d <\/p>\n<p>            ( <\/p>\n<p>              s <\/p>\n<p>              \u02d9 <\/p>\n<p>              n <\/p>\n<p>              \u2212 <\/p>\n<p>              1 <\/p>\n<p>            \u2212 <\/p>\n<p>              s <\/p>\n<p>              \u02d9 <\/p>\n<p>              e <\/p>\n<p>              n <\/p>\n<p>              d <\/p>\n<p>            ) <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>           w <\/p>\n<p>            a <\/p>\n<p>            , <\/p>\n<p>             e <\/p>\n<p>             n <\/p>\n<p>             d <\/p>\n<p>            ( <\/p>\n<p>              s <\/p>\n<p>              \u00a8 <\/p>\n<p>             n <\/p>\n<p>            \u2212 <\/p>\n<p>              s <\/p>\n<p>              \u00a8 <\/p>\n<p>              e <\/p>\n<p>              n <\/p>\n<p>              d <\/p>\n<p>            ) <\/p>\n<p>           2 <\/p>\n<p>         J&#061;\\\\sum_{i&#061;0}^{n-2}{\\\\left( w_s\\\\left( s_i-s_{i,\\\\mathrm{ref}} \\\\right) ^2&#043;w_v\\\\left( \\\\dot{s}_i-\\\\dot{s}_{i,\\\\mathrm{ref}} \\\\right) ^2&#043;w_a\\\\ddot{s}_{i}^{2}&#043;w_j{s}_{i}^{(3)2} \\\\right)}\\\\\\\\&#043;w_{s,\\\\mathrm{end}}\\\\left( s_{n-1}-s_{\\\\mathrm{end}} \\\\right) ^2&#043;w_{v,\\\\mathrm{end}}\\\\left( \\\\dot{s}_{n-1}-\\\\dot{s}_{\\\\mathrm{end}} \\\\right) ^2&#043;w_{a,\\\\mathrm{end}}\\\\left( \\\\ddot{s}_n-\\\\ddot{s}_{\\\\mathrm{end}} \\\\right) ^2 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em;vertical-align: 0em\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em\">J<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.07878em;vertical-align: -1.27767em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em\"><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em\"><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.42314em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">3<\/span><span class=\"mclose mtight\">)<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.276864em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em;vertical-align: -0.08333em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24012em;vertical-align: -0.286108em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em\"><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24012em;vertical-align: -0.286108em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em\"><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24012em;vertical-align: -0.286108em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">(<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">)<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em\"><span class=\"\" style=\"top: -3.2029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u901a\u8fc7<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>           s <\/p>\n<p>           i <\/p>\n<p>            ( <\/p>\n<p>            3 <\/p>\n<p>            ) <\/p>\n<p>          &#061; <\/p>\n<p>              s <\/p>\n<p>              \u00a8 <\/p>\n<p>              i <\/p>\n<p>              &#043; <\/p>\n<p>              1 <\/p>\n<p>            \u2212 <\/p>\n<p>              s <\/p>\n<p>              \u00a8 <\/p>\n<p>             i <\/p>\n<p>            \u0394 <\/p>\n<p>            t <\/p>\n<p>         {s}_i^{(3)}&#061;\\\\frac{\\\\ddot{s}_{i&#043;1}-\\\\ddot{s}_i}{\\\\Delta t} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.32166em;vertical-align: -0.276864em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.42314em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">3<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.276864em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.03086em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.34486em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u9690\u5f0f\u5730\u6d88\u9664\u52a0\u52a0\u901f\u5ea6\u53d8\u91cf&#xff0c;\u4ee3\u5165\u4ee3\u4ef7\u51fd\u6570\u5e76\u6d88\u9664\u5e38\u6570\u9879\u53ef\u5316\u7b80\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>              J <\/p>\n<p>              &#061; <\/p>\n<p>               w <\/p>\n<p>               s <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                0 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>               s <\/p>\n<p>               i <\/p>\n<p>               2 <\/p>\n<p>              &#043; <\/p>\n<p>               w <\/p>\n<p>                s <\/p>\n<p>                , <\/p>\n<p>                 e <\/p>\n<p>                 n <\/p>\n<p>                 d <\/p>\n<p>               s <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>               2 <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>               w <\/p>\n<p>               s <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                0 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                s <\/p>\n<p>                 i <\/p>\n<p>                 , <\/p>\n<p>                  r <\/p>\n<p>                  e <\/p>\n<p>                  f <\/p>\n<p>                s <\/p>\n<p>                i <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>               w <\/p>\n<p>                s <\/p>\n<p>                , <\/p>\n<p>                 e <\/p>\n<p>                 n <\/p>\n<p>                 d <\/p>\n<p>               s <\/p>\n<p>                e <\/p>\n<p>                n <\/p>\n<p>                d <\/p>\n<p>               s <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>              &#043; <\/p>\n<p>               w <\/p>\n<p>               v <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                0 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                s <\/p>\n<p>                \u02d9 <\/p>\n<p>               i <\/p>\n<p>               2 <\/p>\n<p>              &#043; <\/p>\n<p>               w <\/p>\n<p>                v <\/p>\n<p>                , <\/p>\n<p>                 e <\/p>\n<p>                 n <\/p>\n<p>                 d <\/p>\n<p>                s <\/p>\n<p>                \u02d9 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>               2 <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>               w <\/p>\n<p>               v <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                0 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                 i <\/p>\n<p>                 , <\/p>\n<p>                  r <\/p>\n<p>                  e <\/p>\n<p>                  f <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                i <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>               w <\/p>\n<p>                v <\/p>\n<p>                , <\/p>\n<p>                 e <\/p>\n<p>                 n <\/p>\n<p>                 d <\/p>\n<p>                s <\/p>\n<p>                \u02d9 <\/p>\n<p>                e <\/p>\n<p>                n <\/p>\n<p>                d <\/p>\n<p>                s <\/p>\n<p>                \u02d9 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>              &#043; <\/p>\n<p>               ( <\/p>\n<p>                w <\/p>\n<p>                a <\/p>\n<p>               &#043; <\/p>\n<p>                 w <\/p>\n<p>                 j <\/p>\n<p>                 \u0394 <\/p>\n<p>                  t <\/p>\n<p>                  2 <\/p>\n<p>               ) <\/p>\n<p>                s <\/p>\n<p>                \u00a8 <\/p>\n<p>               0 <\/p>\n<p>               2 <\/p>\n<p>              &#043; <\/p>\n<p>               ( <\/p>\n<p>                w <\/p>\n<p>                a <\/p>\n<p>               &#043; <\/p>\n<p>                w <\/p>\n<p>                 a <\/p>\n<p>                 , <\/p>\n<p>                  e <\/p>\n<p>                  n <\/p>\n<p>                  d <\/p>\n<p>               &#043; <\/p>\n<p>                 w <\/p>\n<p>                 j <\/p>\n<p>                 \u0394 <\/p>\n<p>                  t <\/p>\n<p>                  2 <\/p>\n<p>               ) <\/p>\n<p>                s <\/p>\n<p>                \u00a8 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>               2 <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>               w <\/p>\n<p>                a <\/p>\n<p>                , <\/p>\n<p>                 e <\/p>\n<p>                 n <\/p>\n<p>                 d <\/p>\n<p>                s <\/p>\n<p>                \u00a8 <\/p>\n<p>                e <\/p>\n<p>                n <\/p>\n<p>                d <\/p>\n<p>                s <\/p>\n<p>                \u00a8 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                1 <\/p>\n<p>              &#043; <\/p>\n<p>               ( <\/p>\n<p>                w <\/p>\n<p>                a <\/p>\n<p>               &#043; <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                  j <\/p>\n<p>                 \u0394 <\/p>\n<p>                  t <\/p>\n<p>                  2 <\/p>\n<p>               ) <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                1 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                s <\/p>\n<p>                \u00a8 <\/p>\n<p>               i <\/p>\n<p>               2 <\/p>\n<p>              \u2212 <\/p>\n<p>                2 <\/p>\n<p>                 w <\/p>\n<p>                 j <\/p>\n<p>                \u0394 <\/p>\n<p>                 t <\/p>\n<p>                 2 <\/p>\n<p>               \u2211 <\/p>\n<p>                i <\/p>\n<p>                &#061; <\/p>\n<p>                0 <\/p>\n<p>                n <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                i <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                 i <\/p>\n<p>                 &#043; <\/p>\n<p>                 1 <\/p>\n<p>         \\\\begin{aligned}J&#061;&amp;w_s\\\\sum_{i&#061;0}^{n-2}{s_{i}^{2}}&#043;w_{s,\\\\mathrm{end}}s_{n-1}^{2}-2w_s\\\\sum_{i&#061;0}^{n-2}{s_{i,\\\\mathrm{ref}}s_i}-2w_{s,\\\\mathrm{end}}s_{\\\\mathrm{end}}s_{n-1}\\\\\\\\&amp;&#043;w_v\\\\sum_{i&#061;0}^{n-2}{\\\\dot{s}_{i}^{2}}&#043;w_{v,\\\\mathrm{end}}\\\\dot{s}_{n-1}^{2}-2w_v\\\\sum_{i&#061;0}^{n-2}{\\\\dot{s}_{i,\\\\mathrm{ref}}\\\\dot{s}_i}-2w_{v,\\\\mathrm{end}}\\\\dot{s}_{\\\\mathrm{end}}\\\\dot{s}_{n-1}\\\\\\\\&amp;&#043;\\\\left( w_a&#043;\\\\frac{w_j}{\\\\Delta t^2} \\\\right) \\\\ddot{s}_{0}^{2}&#043;\\\\left( w_a&#043;w_{a,\\\\mathrm{end}}&#043;\\\\frac{w_j}{\\\\Delta t^2} \\\\right) \\\\ddot{s}_{n-1}^{2}-2w_{a,\\\\mathrm{end}}\\\\ddot{s}_{\\\\mathrm{end}}\\\\ddot{s}_{n-1}\\\\\\\\&amp;&#043;\\\\left( w_a&#043;\\\\frac{2w_j}{\\\\Delta t^2} \\\\right) \\\\sum_{i&#061;1}^{n-2}{\\\\ddot{s}_{i}^{2}}-\\\\frac{2w_j}{\\\\Delta t^2}\\\\sum_{i&#061;0}^{n-2}{\\\\ddot{s}_i\\\\ddot{s}_{i&#043;1}}\\\\end{aligned} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 12.2723em;vertical-align: -5.88617em\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 6.38617em\"><span class=\"\" style=\"top: -8.38617em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em\">J<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><\/span><span class=\"\" style=\"top: -5.00739em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -2.27972em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: 0.507391em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 5.88617em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 6.38617em\"><span class=\"\" style=\"top: -8.38617em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.305331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -5.00739em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.305331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.27972em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10756em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10756em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.305331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: 0.507391em\"><span class=\"pstrut\" style=\"height: 3.80111em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.864108em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.740108em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.80111em\"><span class=\"\" style=\"top: -1.87233em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05001em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.27767em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 5.88617em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ece\u800c\u5f97\u5230\u6838\u77e9\u9635<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          P <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 P <\/p>\n<p>                 s <\/p>\n<p>                 P <\/p>\n<p>                  s <\/p>\n<p>                  \u02d9 <\/p>\n<p>                 P <\/p>\n<p>                  s <\/p>\n<p>                  \u00a8 <\/p>\n<p>            ] <\/p>\n<p>            3 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            3 <\/p>\n<p>            n <\/p>\n<p>         \\\\boldsymbol{P}&#061;\\\\left[ \\\\begin{matrix} \\\\boldsymbol{P}_s&amp; &amp; \\\\\\\\ &amp; \\\\boldsymbol{P}_{\\\\dot{s}}&amp; \\\\\\\\ &amp; &amp; \\\\boldsymbol{P}_{\\\\ddot{s}}\\\\\\\\\\\\end{matrix} \\\\right] _{3n\\\\times 3n} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68611em;vertical-align: 0em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.15972em\">P<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.70807em;vertical-align: -1.65805em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.15972em\">P<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.15972em\">P<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\"><span class=\"mtight\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.15972em\">P<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\"><span class=\"mtight\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\" style=\"top: -1.10028em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.65805em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u548c\u504f\u7f6e\u5411\u91cf<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          q <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                  s <\/p>\n<p>                  s <\/p>\n<p>                   0 <\/p>\n<p>                   , <\/p>\n<p>                    r <\/p>\n<p>                    e <\/p>\n<p>                    f <\/p>\n<p>                \u22ee <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                  s <\/p>\n<p>                  s <\/p>\n<p>                   n <\/p>\n<p>                   \u2212 <\/p>\n<p>                   2 <\/p>\n<p>                   , <\/p>\n<p>                    r <\/p>\n<p>                    e <\/p>\n<p>                    f <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                   s <\/p>\n<p>                   , <\/p>\n<p>                    e <\/p>\n<p>                    n <\/p>\n<p>                    d <\/p>\n<p>                  s <\/p>\n<p>                   e <\/p>\n<p>                   n <\/p>\n<p>                   d <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                  v <\/p>\n<p>                   s <\/p>\n<p>                   \u02d9 <\/p>\n<p>                   0 <\/p>\n<p>                   , <\/p>\n<p>                    r <\/p>\n<p>                    e <\/p>\n<p>                    f <\/p>\n<p>                \u22ee <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                  v <\/p>\n<p>                   s <\/p>\n<p>                   \u02d9 <\/p>\n<p>                   n <\/p>\n<p>                   \u2212 <\/p>\n<p>                   2 <\/p>\n<p>                   , <\/p>\n<p>                    r <\/p>\n<p>                    e <\/p>\n<p>                    f <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                   v <\/p>\n<p>                   , <\/p>\n<p>                    e <\/p>\n<p>                    n <\/p>\n<p>                    d <\/p>\n<p>                   s <\/p>\n<p>                   \u02d9 <\/p>\n<p>                   e <\/p>\n<p>                   n <\/p>\n<p>                   d <\/p>\n<p>                0 <\/p>\n<p>                \u22ee <\/p>\n<p>                0 <\/p>\n<p>                 \u2212 <\/p>\n<p>                 2 <\/p>\n<p>                  w <\/p>\n<p>                   a <\/p>\n<p>                   , <\/p>\n<p>                    e <\/p>\n<p>                    n <\/p>\n<p>                    d <\/p>\n<p>                   s <\/p>\n<p>                   \u00a8 <\/p>\n<p>                   e <\/p>\n<p>                   n <\/p>\n<p>                   d <\/p>\n<p>            ] <\/p>\n<p>            3 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            1 <\/p>\n<p>         \\\\boldsymbol{q}&#061;\\\\left[ \\\\begin{array}{c} -2w_ss_{0,\\\\mathrm{ref}}\\\\\\\\ \\\\vdots\\\\\\\\ -2w_ss_{n-2,\\\\mathrm{ref}}\\\\\\\\ -2w_{s,\\\\mathrm{end}}s_{\\\\mathrm{end}}\\\\\\\\ \\\\hline -2w_v\\\\dot{s}_{0,\\\\mathrm{ref}}\\\\\\\\ \\\\vdots\\\\\\\\ -2w_v\\\\dot{s}_{n-2,\\\\mathrm{ref}}\\\\\\\\ -2w_{v,\\\\mathrm{end}}\\\\dot{s}_{\\\\mathrm{end}}\\\\\\\\ \\\\hline 0\\\\\\\\ \\\\vdots\\\\\\\\ 0\\\\\\\\ -2w_{a,\\\\mathrm{end}}\\\\ddot{s}_{\\\\mathrm{end}}\\\\\\\\\\\\end{array} \\\\right] _{3n\\\\times 1} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.63888em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.03704em\">q<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 16.488em;vertical-align: -8.04803em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 8.37092em\"><span class=\"\" style=\"top: 4.0501em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: 2.8951em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: 2.2941em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: 1.6931em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: 1.0921em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: 0.491105em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -0.109895em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -0.710895em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -1.3119em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -1.9129em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.5139em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.1149em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.7159em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3169em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -4.9179em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -5.5189em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -6.1199em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -6.7209em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -7.3219em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -7.9229em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -8.5239em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -9.1249em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a2<\/span><\/span><\/span><span class=\"\" style=\"top: -10.3709em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 7.85012em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 8.44em\"><span class=\"\" style=\"top: -10.44em\"><span class=\"pstrut\" style=\"height: 10.44em\"><\/span><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 8.44em\"><span class=\"\" style=\"top: -11.2875em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -9.4275em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\">\u22ee<\/span><span class=\"mord rule\" style=\"border-right-width: 0em;border-top-width: 1.5em;bottom: 0em\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -8.2275em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -7.0275em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">s<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -5.8275em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.9675em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\">\u22ee<\/span><span class=\"mord rule\" style=\"border-right-width: 0em;border-top-width: 1.5em;bottom: 0em\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.7675em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">r<\/span><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.07778em\">f<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.5675em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -0.3675em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: 1.4925em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\">\u22ee<\/span><span class=\"mord rule\" style=\"border-right-width: 0em;border-top-width: 1.5em;bottom: 0em\"><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: 2.6925em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: 3.8925em\"><span class=\"pstrut\" style=\"height: 3.6875em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.02691em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.02691em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">a<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">e<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 7.94em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -7.96em\"><span class=\"pstrut\" style=\"height: 10.44em\"><\/span><span class=\"hline\" style=\"border-bottom-width: 0.05em\"><\/span><\/span><span class=\"\" style=\"top: -13.42em\"><span class=\"pstrut\" style=\"height: 10.44em\"><\/span><span class=\"hline\" style=\"border-bottom-width: 0.05em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 7.94em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 8.37092em\"><span class=\"\" style=\"top: 4.0501em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: 2.8951em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: 2.2941em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: 1.6931em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: 1.0921em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: 0.491105em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -0.109895em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -0.710895em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -1.3119em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -1.9129em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.5139em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.1149em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -3.7159em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3169em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -4.9179em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -5.5189em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -6.1199em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -6.7209em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -7.3219em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -7.9229em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -8.5239em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -9.1249em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a5<\/span><\/span><\/span><span class=\"\" style=\"top: -10.3709em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 7.85012em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\" style=\"top: 5.2897em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 8.04803em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>2.3 \u7ea6\u675f\u6761\u4ef6<\/h3>\n<p>\u6839\u636e\u8fd0\u52a8\u5b66\u516c\u5f0f\u53ef\u5f97\u8fd0\u52a8\u5b66\u7b49\u5f0f\u7ea6\u675f<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          { <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                 i <\/p>\n<p>                 &#043; <\/p>\n<p>                 1 <\/p>\n<p>               &#061; <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                i <\/p>\n<p>               &#043; <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>               t <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                2 <\/p>\n<p>                j <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>                t <\/p>\n<p>                2 <\/p>\n<p>               &#061; <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                i <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                2 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>               t <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                2 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                 i <\/p>\n<p>                 &#043; <\/p>\n<p>                 1 <\/p>\n<p>               \u0394 <\/p>\n<p>               t <\/p>\n<p>                s <\/p>\n<p>                 i <\/p>\n<p>                 &#043; <\/p>\n<p>                 1 <\/p>\n<p>               &#061; <\/p>\n<p>                s <\/p>\n<p>                i <\/p>\n<p>               &#043; <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>               t <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                2 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>                t <\/p>\n<p>                2 <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                6 <\/p>\n<p>                j <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>                t <\/p>\n<p>                3 <\/p>\n<p>               &#061; <\/p>\n<p>                s <\/p>\n<p>                i <\/p>\n<p>               &#043; <\/p>\n<p>                 s <\/p>\n<p>                 \u02d9 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>               t <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                3 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                i <\/p>\n<p>               \u0394 <\/p>\n<p>                t <\/p>\n<p>                2 <\/p>\n<p>               &#043; <\/p>\n<p>                1 <\/p>\n<p>                6 <\/p>\n<p>                 s <\/p>\n<p>                 \u00a8 <\/p>\n<p>                 i <\/p>\n<p>                 &#043; <\/p>\n<p>                 1 <\/p>\n<p>               \u0394 <\/p>\n<p>                t <\/p>\n<p>                3 <\/p>\n<p>         \\\\begin{cases} \\\\dot{s}_{i&#043;1}&#061;\\\\dot{s}_i&#043;\\\\ddot{s}_i\\\\Delta t&#043;\\\\frac{1}{2}j_i\\\\Delta t^2&#061;\\\\dot{s}_i&#043;\\\\frac{1}{2}\\\\ddot{s}_i\\\\Delta t&#043;\\\\frac{1}{2}\\\\ddot{s}_{i&#043;1}\\\\Delta t\\\\\\\\ s_{i&#043;1}&#061;s_i&#043;\\\\dot{s}_i\\\\Delta t&#043;\\\\frac{1}{2}\\\\ddot{s}_i\\\\Delta t^2&#043;\\\\frac{1}{6}j_i\\\\Delta t^3&#061;s_i&#043;\\\\dot{s}_i\\\\Delta t&#043;\\\\frac{1}{3}\\\\ddot{s}_i\\\\Delta t^2&#043;\\\\frac{1}{6}\\\\ddot{s}_{i&#043;1}\\\\Delta t^3\\\\\\\\\\\\end{cases} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 3.00003em;vertical-align: -1.25003em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size4\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em\"><span class=\"\" style=\"top: -3.69em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em\">j<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.05724em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.008em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em\">j<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.05724em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathdefault\">t<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7ea6\u675f\u521d\u59cb\u72b6\u6001<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>           0 <\/p>\n<p>          &#061; <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>            i <\/p>\n<p>            n <\/p>\n<p>            i <\/p>\n<p>            t <\/p>\n<p>          , <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>           0 <\/p>\n<p>          &#061; <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>            i <\/p>\n<p>            n <\/p>\n<p>            i <\/p>\n<p>            t <\/p>\n<p>          , <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           0 <\/p>\n<p>          &#061; <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>            i <\/p>\n<p>            n <\/p>\n<p>            i <\/p>\n<p>            t <\/p>\n<p>         \\\\dot{s}_0&#061;\\\\dot{s}_{\\\\mathrm{init}}, \\\\dot{s}_0&#061;\\\\dot{s}_{\\\\mathrm{init}}, \\\\ddot{s}_0&#061;\\\\ddot{s}_{\\\\mathrm{init}} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.81786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.81786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6b64\u5916\u8fd8\u9700\u4fdd\u8bc1\u5404\u9636\u72b6\u6001\u91cf\u6ee1\u8db3\u4e0d\u7b49\u5f0f\u7ea6\u675f<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>           s <\/p>\n<p>           min <\/p>\n<p>           \u2061 <\/p>\n<p>          \u2a7d <\/p>\n<p>           s <\/p>\n<p>           i <\/p>\n<p>          \u2a7d <\/p>\n<p>           s <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>          , <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>           min <\/p>\n<p>           \u2061 <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>           i <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u02d9 <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>          , <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           min <\/p>\n<p>           \u2061 <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           i <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>          , <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           min <\/p>\n<p>           \u2061 <\/p>\n<p>            ( <\/p>\n<p>            3 <\/p>\n<p>            ) <\/p>\n<p>          \u0394 <\/p>\n<p>          t <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>            i <\/p>\n<p>            &#043; <\/p>\n<p>            1 <\/p>\n<p>          \u2212 <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           i <\/p>\n<p>          \u2a7d <\/p>\n<p>            s <\/p>\n<p>            \u00a8 <\/p>\n<p>           max <\/p>\n<p>           \u2061 <\/p>\n<p>            ( <\/p>\n<p>            3 <\/p>\n<p>            ) <\/p>\n<p>          \u0394 <\/p>\n<p>          t <\/p>\n<p>         s_{\\\\min}\\\\leqslant s_i\\\\leqslant s_{\\\\max}, \\\\dot{s}_{\\\\min}\\\\leqslant \\\\dot{s}_i\\\\leqslant \\\\dot{s}_{\\\\max}, \\\\ddot{s}_{\\\\min}\\\\leqslant \\\\ddot{s}_i\\\\leqslant \\\\ddot{s}_{\\\\max}, \\\\ddot{s}_{\\\\min}^{(3)}\\\\Delta t\\\\leqslant \\\\ddot{s}_{i&#043;1}-\\\\ddot{s}_i\\\\leqslant \\\\ddot{s}_{\\\\max}^{(3)}\\\\Delta t <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.78667em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.3175em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.4675em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">min<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.78667em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.15139em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.30139em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">max<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.3175em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.4675em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">min<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.81786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8623em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.08333em\">\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.15139em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.30139em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">max<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.3175em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.4675em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">min<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.81786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.3275em;vertical-align: -0.282702em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.15139em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.30139em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">max<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0448em\"><span class=\"\" style=\"top: -2.4173em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">min<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">3<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.282702em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.876191em;vertical-align: -0.208331em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.81786em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.185em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.19444em\">\u00a8<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.938em\"><span class=\"\" style=\"top: -2.453em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mop mtight\">max<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\">3<\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord mathdefault\">t<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ece\u800c\u5f97\u5230\u7ea6\u675f\u77e9\u9635<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          A <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 A <\/p>\n<p>                   i <\/p>\n<p>                   n <\/p>\n<p>                   i <\/p>\n<p>                   t <\/p>\n<p>                  , <\/p>\n<p>                  3 <\/p>\n<p>                  \u00d7 <\/p>\n<p>                  3 <\/p>\n<p>                  n <\/p>\n<p>                 A <\/p>\n<p>                   b <\/p>\n<p>                   o <\/p>\n<p>                   u <\/p>\n<p>                   n <\/p>\n<p>                   d <\/p>\n<p>                  , <\/p>\n<p>                  3 <\/p>\n<p>                  n <\/p>\n<p>                  &#043; <\/p>\n<p>                   ( <\/p>\n<p>                   n <\/p>\n<p>                   \u2212 <\/p>\n<p>                   1 <\/p>\n<p>                   ) <\/p>\n<p>                  \u00d7 <\/p>\n<p>                  3 <\/p>\n<p>                  n <\/p>\n<p>                 A <\/p>\n<p>                   s <\/p>\n<p>                   y <\/p>\n<p>                   s <\/p>\n<p>                  , <\/p>\n<p>                  2 <\/p>\n<p>                   ( <\/p>\n<p>                   n <\/p>\n<p>                   \u2212 <\/p>\n<p>                   1 <\/p>\n<p>                   ) <\/p>\n<p>                  \u00d7 <\/p>\n<p>                  3 <\/p>\n<p>                  n <\/p>\n<p>            ] <\/p>\n<p>            6 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            3 <\/p>\n<p>            n <\/p>\n<p>          , <\/p>\n<p>          l <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 l <\/p>\n<p>                  i <\/p>\n<p>                  n <\/p>\n<p>                  i <\/p>\n<p>                  t <\/p>\n<p>                 l <\/p>\n<p>                  b <\/p>\n<p>                  o <\/p>\n<p>                  u <\/p>\n<p>                  n <\/p>\n<p>                  d <\/p>\n<p>                 l <\/p>\n<p>                  s <\/p>\n<p>                  y <\/p>\n<p>                  s <\/p>\n<p>            ] <\/p>\n<p>            6 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            1 <\/p>\n<p>          , <\/p>\n<p>          u <\/p>\n<p>          &#061; <\/p>\n<p>            [ <\/p>\n<p>                 u <\/p>\n<p>                  i <\/p>\n<p>                  n <\/p>\n<p>                  i <\/p>\n<p>                  t <\/p>\n<p>                 u <\/p>\n<p>                  b <\/p>\n<p>                  o <\/p>\n<p>                  u <\/p>\n<p>                  n <\/p>\n<p>                  d <\/p>\n<p>                 u <\/p>\n<p>                  s <\/p>\n<p>                  y <\/p>\n<p>                  s <\/p>\n<p>            ] <\/p>\n<p>            6 <\/p>\n<p>            n <\/p>\n<p>            \u00d7 <\/p>\n<p>            1 <\/p>\n<p>         \\\\boldsymbol{A}&#061;\\\\left[ \\\\begin{array}{c} \\\\boldsymbol{A}_{\\\\mathrm{init}, 3\\\\times 3n}\\\\\\\\ \\\\boldsymbol{A}_{\\\\mathrm{bound}, 3n&#043;\\\\left( n-1 \\\\right) \\\\times 3n}\\\\\\\\ \\\\boldsymbol{A}_{\\\\mathrm{sys}, 2\\\\left( n-1 \\\\right) \\\\times 3n}\\\\\\\\\\\\end{array} \\\\right] _{6n\\\\times 3n}, \\\\boldsymbol{l}&#061;\\\\left[ \\\\begin{array}{c} \\\\boldsymbol{l}_{\\\\mathrm{init}}\\\\\\\\ \\\\boldsymbol{l}_{\\\\mathrm{bound}}\\\\\\\\ \\\\boldsymbol{l}_{\\\\mathrm{sys}}\\\\\\\\\\\\end{array} \\\\right] _{6n\\\\times 1}, \\\\boldsymbol{u}&#061;\\\\left[ \\\\begin{array}{c} \\\\boldsymbol{u}_{\\\\mathrm{init}}\\\\\\\\ \\\\boldsymbol{u}_{\\\\mathrm{bound}}\\\\\\\\ \\\\boldsymbol{u}_{\\\\mathrm{sys}}\\\\\\\\\\\\end{array} \\\\right] _{6n\\\\times 1} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68611em;vertical-align: 0em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">A<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.70807em;vertical-align: -1.65805em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">A<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\">3<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">A<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">b<\/span><span class=\"mord mathrm mtight\">o<\/span><span class=\"mord mathrm mtight\">u<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">&#043;<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">)<\/span><\/span><\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">A<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3448em\"><span class=\"\" style=\"top: -2.5198em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">s<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.01389em\">y<\/span><span class=\"mord mathrm mtight\">s<\/span><\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\">2<\/span><span class=\"minner mtight\"><span class=\"mopen mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">(<\/span><\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><span class=\"mclose mtight delimcenter\" style=\"top: 0em\"><span class=\"mtight\">)<\/span><\/span><\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3552em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\" style=\"top: -1.10028em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">3<\/span><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.65805em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.0088em\">l<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.70807em;vertical-align: -1.65805em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.0088em\">l<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.0088em\">l<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">b<\/span><span class=\"mord mathrm mtight\">o<\/span><span class=\"mord mathrm mtight\">u<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.0088em\">l<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">s<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.01389em\">y<\/span><span class=\"mord mathrm mtight\">s<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\" style=\"top: -1.10028em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.65805em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">u<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.70807em;vertical-align: -1.65805em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a3<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05em\"><span class=\"\" style=\"top: -4.21em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">u<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317502em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">i<\/span><span class=\"mord mathrm mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.01em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">u<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">b<\/span><span class=\"mord mathrm mtight\">o<\/span><span class=\"mord mathrm mtight\">u<\/span><span class=\"mord mathrm mtight\">n<\/span><span class=\"mord mathrm mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -1.81em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">u<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathrm mtight\">s<\/span><span class=\"mord mathrm mtight\" style=\"margin-right: 0.01389em\">y<\/span><span class=\"mord mathrm mtight\">s<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><\/span><\/span><span class=\"mclose\"><span class=\"delimsizing mult\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 2.05002em\"><span class=\"\" style=\"top: -2.25em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a6<\/span><\/span><\/span><span class=\"\" style=\"top: -4.05002em\"><span class=\"pstrut\" style=\"height: 3.155em\"><\/span><span class=\"delimsizinginner delim-size4\"><span class=\"\">\u23a4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.55002em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"\" style=\"top: -1.10028em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">6<\/span><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.65805em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>2.4 \u4e8c\u6b21\u89c4\u5212\u5f62\u5f0f<\/h3>\n<p>\u7efc\u4e0a\u6240\u8ff0&#xff0c;\u53ef\u5f97\u5230PJSO\u7b97\u6cd5\u7684\u4e8c\u6b21\u89c4\u5212\u5f62\u5f0f<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>            min <\/p>\n<p>            \u2061 <\/p>\n<p>           x <\/p>\n<p>          J <\/p>\n<p>          &#061; <\/p>\n<p>           x <\/p>\n<p>           T <\/p>\n<p>           P <\/p>\n<p>           x <\/p>\n<p>          &#043; <\/p>\n<p>           q <\/p>\n<p>           T <\/p>\n<p>          x <\/p>\n<p>          s <\/p>\n<p>          . <\/p>\n<p>          t <\/p>\n<p>          . <\/p>\n<p>          l <\/p>\n<p>          \u2a7d <\/p>\n<p>           A <\/p>\n<p>           x <\/p>\n<p>          \u2a7d <\/p>\n<p>          u <\/p>\n<p>         \\\\min _{\\\\boldsymbol{x}}J&#061;\\\\boldsymbol{x}^T\\\\boldsymbol{Px}&#043;\\\\boldsymbol{q}^T\\\\boldsymbol{x}\\\\\\\\\\\\mathrm{s}.\\\\mathrm{t}. \\\\boldsymbol{l}\\\\leqslant \\\\boldsymbol{Ax}\\\\leqslant \\\\boldsymbol{u} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.38333em;vertical-align: -0.7em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.66786em\"><span class=\"\" style=\"top: -2.1em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord boldsymbol mtight\">x<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.7em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.09618em\">J<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.974661em;vertical-align: -0.08333em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.15972em\">P<\/span><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.08577em;vertical-align: -0.19444em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.03704em\">q<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.891331em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.13889em\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83111em;vertical-align: -0.13667em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">s<\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span class=\"mord mathrm\">t<\/span><\/span><span class=\"mord\">.<\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.0088em\">l<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.82278em;vertical-align: -0.13667em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">A<\/span><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.44444em;vertical-align: 0em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">u<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2>3 \u7b97\u6cd5\u4eff\u771f<\/h2>\n<h3>3.1 ROS C&#043;&#043;\u4eff\u771f<\/h3>\n<p>\u6838\u5fc3\u4ee3\u7801\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><span class=\"token keyword\">bool<\/span> <span class=\"token class-name\">PiecewiseJerkVelocityPlanner<\/span><span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">plan<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Points3d<span class=\"token operator\">&amp;<\/span> waypoints<span class=\"token punctuation\">,<\/span> VelocityProfile<span class=\"token operator\">&amp;<\/span> velocity_profile<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n  <span class=\"token keyword\">int<\/span> dim <span class=\"token operator\">&#061;<\/span> <span class=\"token generic-function\"><span class=\"token function\">static_cast<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span>waypoints<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">double<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">s_ref<\/span><span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0.0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> dim<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span><br \/>\n  <span class=\"token punctuation\">{<\/span><br \/>\n    s_ref<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span><br \/>\n        s_ref<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> std<span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">hypot<\/span><span class=\"token punctuation\">(<\/span>waypoints<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">x<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> waypoints<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">x<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> waypoints<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">y<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> waypoints<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">y<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token punctuation\">}<\/span><br \/>\n  x_max_ <span class=\"token operator\">&#061;<\/span> s_ref<span class=\"token punctuation\">.<\/span><span class=\"token function\">back<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  <span class=\"token comment\">\/\/ construct QP Problem<\/span><br \/>\n  Eigen<span class=\"token double-colon punctuation\">::<\/span>MatrixXd P<span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_float<span class=\"token operator\">&gt;<\/span> l<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> q<span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">_calKernel<\/span><span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">,<\/span> P<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">_calOffset<\/span><span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">,<\/span> s_ref<span class=\"token punctuation\">,<\/span> q<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">_calAffineConstraint<\/span><span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">_calBoundary<\/span><span class=\"token punctuation\">(<\/span>dim<span class=\"token punctuation\">,<\/span> s_ref<span class=\"token punctuation\">,<\/span> l<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_float<span class=\"token operator\">&gt;<\/span> P_data<span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_int<span class=\"token operator\">&gt;<\/span> P_indices<span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_int<span class=\"token operator\">&gt;<\/span> P_indptr<span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">int<\/span> ind_P <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> col <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> col <span class=\"token operator\">&lt;<\/span> P<span class=\"token punctuation\">.<\/span><span class=\"token function\">cols<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>col<span class=\"token punctuation\">)<\/span><br \/>\n  <span class=\"token punctuation\">{<\/span><br \/>\n    P_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>ind_P<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> row <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> row <span class=\"token operator\">&lt;&#061;<\/span> col<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>row<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n      P_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">P<\/span><span class=\"token punctuation\">(<\/span>row<span class=\"token punctuation\">,<\/span> col<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n      P_indices<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>row<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n      ind_P<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n  <span class=\"token punctuation\">}<\/span><br \/>\n  P_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>ind_P<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_float<span class=\"token operator\">&gt;<\/span> A_data<span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_int<span class=\"token operator\">&gt;<\/span> A_indices<span class=\"token punctuation\">;<\/span><br \/>\n  std<span class=\"token double-colon punctuation\">::<\/span>vector<span class=\"token operator\">&lt;<\/span>c_int<span class=\"token operator\">&gt;<\/span> A_indptr<span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">int<\/span> ind_A <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> col <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> col <span class=\"token operator\">&lt;<\/span> A<span class=\"token punctuation\">.<\/span><span class=\"token function\">cols<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>col<span class=\"token punctuation\">)<\/span><br \/>\n  <span class=\"token punctuation\">{<\/span><br \/>\n    A_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>ind_A<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> row <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> row <span class=\"token operator\">&lt;<\/span> A<span class=\"token punctuation\">.<\/span><span class=\"token function\">rows<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>row<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n      <span class=\"token keyword\">double<\/span> data <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">A<\/span><span class=\"token punctuation\">(<\/span>row<span class=\"token punctuation\">,<\/span> col<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n      <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>std<span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">fabs<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&gt;<\/span> kMathEpsilon<span class=\"token punctuation\">)<\/span><br \/>\n      <span class=\"token punctuation\">{<\/span><br \/>\n        A_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        A_indices<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>row<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token operator\">&#043;&#043;<\/span>ind_A<span class=\"token punctuation\">;<\/span><br \/>\n      <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n  <span class=\"token punctuation\">}<\/span><br \/>\n  A_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>ind_A<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  <span class=\"token comment\">\/\/ solve<\/span><br \/>\n  OSQPWorkspace<span class=\"token operator\">*<\/span> work <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">nullptr<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  OSQPData<span class=\"token operator\">*<\/span> data <span class=\"token operator\">&#061;<\/span> <span class=\"token generic-function\"><span class=\"token function\">reinterpret_cast<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>OSQPData<span class=\"token operator\">*<\/span><span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">c_malloc<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>OSQPData<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  OSQPSettings<span class=\"token operator\">*<\/span> settings <span class=\"token operator\">&#061;<\/span> <span class=\"token generic-function\"><span class=\"token function\">reinterpret_cast<\/span><span class=\"token generic class-name\"><span class=\"token operator\">&lt;<\/span>OSQPSettings<span class=\"token operator\">*<\/span><span class=\"token operator\">&gt;<\/span><\/span><\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">c_malloc<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>OSQPSettings<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">osqp_set_default_settings<\/span><span class=\"token punctuation\">(<\/span>settings<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  settings<span class=\"token operator\">-&gt;<\/span>verbose <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  settings<span class=\"token operator\">-&gt;<\/span>warm_start <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>n <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">3<\/span> <span class=\"token operator\">*<\/span> dim<span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>m <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">6<\/span> <span class=\"token operator\">*<\/span> dim<span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>P <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">csc_matrix<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">,<\/span> data<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">,<\/span> P_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> P_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> P_indices<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> P_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>A <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">csc_matrix<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token operator\">-&gt;<\/span>m<span class=\"token punctuation\">,<\/span> data<span class=\"token operator\">-&gt;<\/span>n<span class=\"token punctuation\">,<\/span> A_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> A_data<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> A_indices<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> A_indptr<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>q <span class=\"token operator\">&#061;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>l <span class=\"token operator\">&#061;<\/span> l<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  data<span class=\"token operator\">-&gt;<\/span>u <span class=\"token operator\">&#061;<\/span> u<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">osqp_setup<\/span><span class=\"token punctuation\">(<\/span><span class=\"token operator\">&amp;<\/span>work<span class=\"token punctuation\">,<\/span> data<span class=\"token punctuation\">,<\/span> settings<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">osqp_solve<\/span><span class=\"token punctuation\">(<\/span>work<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">auto<\/span> status <span class=\"token operator\">&#061;<\/span> work<span class=\"token operator\">-&gt;<\/span>info<span class=\"token operator\">-&gt;<\/span>status_val<span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>status <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">||<\/span> <span class=\"token punctuation\">(<\/span>status <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">&amp;&amp;<\/span> status <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n  <span class=\"token punctuation\">{<\/span><br \/>\n    R_DEBUG <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;failed optimization status: &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> work<span class=\"token operator\">-&gt;<\/span>info<span class=\"token operator\">-&gt;<\/span>status<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token punctuation\">}<\/span><\/p>\n<p>  <span class=\"token comment\">\/\/ parse<\/span><br \/>\n  <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> dim<span class=\"token punctuation\">;<\/span> <span class=\"token operator\">&#043;&#043;<\/span>i<span class=\"token punctuation\">)<\/span><br \/>\n  <span class=\"token punctuation\">{<\/span><br \/>\n    velocity_profile<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>dt_ <span class=\"token operator\">*<\/span> i<span class=\"token punctuation\">,<\/span> work<span class=\"token operator\">-&gt;<\/span>solution<span class=\"token operator\">-&gt;<\/span>x<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> work<span class=\"token operator\">-&gt;<\/span>solution<span class=\"token operator\">-&gt;<\/span>x<span class=\"token punctuation\">[<\/span>dim <span class=\"token operator\">&#043;<\/span> i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> work<span class=\"token operator\">-&gt;<\/span>solution<span class=\"token operator\">-&gt;<\/span>x<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> dim <span class=\"token operator\">&#043;<\/span> i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token punctuation\">}<\/span><\/p>\n<p>  <span class=\"token comment\">\/\/ Cleanup<\/span><br \/>\n  <span class=\"token function\">osqp_cleanup<\/span><span class=\"token punctuation\">(<\/span>work<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">c_free<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token operator\">-&gt;<\/span>A<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">c_free<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token operator\">-&gt;<\/span>P<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">c_free<\/span><span class=\"token punctuation\">(<\/span>data<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n  <span class=\"token function\">c_free<\/span><span class=\"token punctuation\">(<\/span>settings<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>  <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p>\u8fd9\u91cc\u8bbe\u7f6e\u521d\u59cb\u901f\u5ea6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          v <\/p>\n<p>          0 <\/p>\n<p>         &#061; <\/p>\n<p>         1.0 <\/p>\n<p>         \u00a0 <\/p>\n<p>         m <\/p>\n<p>         \/ <\/p>\n<p>         s <\/p>\n<p>        v_0&#061;1.0\\\\ m\/s <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.03588em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">.<\/span><span class=\"mord\">0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathdefault\">s<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u521d\u59cb\u52a0\u901f\u5ea6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          a <\/p>\n<p>          0 <\/p>\n<p>         &#061; <\/p>\n<p>         0 <\/p>\n<p>         \u00a0 <\/p>\n<p>         m <\/p>\n<p>         \/ <\/p>\n<p>          s <\/p>\n<p>          2 <\/p>\n<p>        a_0&#061;0\\\\ m\/s^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.06411em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord\">\/<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1b;\u7ec8\u70b9\u901f\u5ea6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          v <\/p>\n<p>          0 <\/p>\n<p>         &#061; <\/p>\n<p>         0.0 <\/p>\n<p>         \u00a0 <\/p>\n<p>         m <\/p>\n<p>         \/ <\/p>\n<p>         s <\/p>\n<p>        v_0&#061;0.0\\\\ m\/s <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.03588em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mord\">.<\/span><span class=\"mord\">0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathdefault\">s<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7ec8\u70b9\u52a0\u901f\u5ea6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          a <\/p>\n<p>          0 <\/p>\n<p>         &#061; <\/p>\n<p>         0 <\/p>\n<p>         \u00a0 <\/p>\n<p>         m <\/p>\n<p>         \/ <\/p>\n<p>          s <\/p>\n<p>          2 <\/p>\n<p>        a_0&#061;0\\\\ m\/s^2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.06411em;vertical-align: -0.25em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mord\">\/<\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/05\/20250530042618-6839336af0880.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"650\" \/><\/p>\n<h3>3.2 Python\u4eff\u771f<\/h3>\n<p>\u6838\u5fc3\u4ee3\u7801\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><span class=\"token keyword\">def<\/span> <span class=\"token function\">process<\/span><span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">,<\/span> path<span class=\"token punctuation\">:<\/span> List<span class=\"token punctuation\">[<\/span>Point3d<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token operator\">&gt;<\/span> List<span class=\"token punctuation\">[<\/span>Dict<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">:<\/span><br \/>\nvelocity_profiles <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><br \/>\npath_segs<span class=\"token punctuation\">,<\/span> path_refs <span class=\"token operator\">&#061;<\/span> PathPlanner<span class=\"token punctuation\">.<\/span>getPathSegments<span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">for<\/span> i<span class=\"token punctuation\">,<\/span> path_seg <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">enumerate<\/span><span class=\"token punctuation\">(<\/span>path_segs<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    s_ref <span class=\"token operator\">&#061;<\/span> path_refs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><br \/>\n    n <span class=\"token operator\">&#061;<\/span> <span class=\"token builtin\">max<\/span><span class=\"token punctuation\">(<\/span><br \/>\n        <span class=\"token builtin\">len<\/span><span class=\"token punctuation\">(<\/span>path_refs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token builtin\">round<\/span><span class=\"token punctuation\">(<\/span><br \/>\n            self<span class=\"token punctuation\">.<\/span>r <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>dx_max <span class=\"token operator\">**<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&#043;<\/span> s_ref<span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span> <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>ddx_max<span class=\"token punctuation\">)<\/span> \\\\<br \/>\n                <span class=\"token operator\">\/<\/span> <span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>dx_max <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>ddx_max <span class=\"token operator\">*<\/span> self<span class=\"token punctuation\">.<\/span>dt<span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">)<\/span><br \/>\n    s_ref <span class=\"token operator\">&#061;<\/span> np<span class=\"token punctuation\">.<\/span>linspace<span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> s_ref<span class=\"token punctuation\">[<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">)<\/span><\/p>\n<p>    <span class=\"token triple-quoted-string string\">&#039;&#039;&#039;<br \/>\n    min x^T P x &#043; q^T x<br \/>\n    s.t. l &lt;&#061; Ax &lt;&#061; u<br \/>\n    &#039;&#039;&#039;<\/span><br \/>\n    P <span class=\"token operator\">&#061;<\/span> sparse<span class=\"token punctuation\">.<\/span>csc_matrix<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>calKernel<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    q <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>calOffset<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> s_ref<span class=\"token punctuation\">)<\/span><br \/>\n    A <span class=\"token operator\">&#061;<\/span> sparse<span class=\"token punctuation\">.<\/span>csc_matrix<span class=\"token punctuation\">(<\/span>self<span class=\"token punctuation\">.<\/span>calAffineConstraint<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    l<span class=\"token punctuation\">,<\/span> u <span class=\"token operator\">&#061;<\/span> self<span class=\"token punctuation\">.<\/span>calBoundary<span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">,<\/span> s_ref<span class=\"token punctuation\">)<\/span><br \/>\n    solver <span class=\"token operator\">&#061;<\/span> osqp<span class=\"token punctuation\">.<\/span>OSQP<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    solver<span class=\"token punctuation\">.<\/span>setup<span class=\"token punctuation\">(<\/span>P<span class=\"token punctuation\">,<\/span> q<span class=\"token punctuation\">,<\/span> A<span class=\"token punctuation\">,<\/span> l<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> verbose<span class=\"token operator\">&#061;<\/span><span class=\"token boolean\">False<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    res <span class=\"token operator\">&#061;<\/span> solver<span class=\"token punctuation\">.<\/span>solve<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    sol <span class=\"token operator\">&#061;<\/span> res<span class=\"token punctuation\">.<\/span>x<\/p>\n<p>    velocity_profiles<span class=\"token punctuation\">.<\/span>append<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token string\">&#034;time&#034;<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token punctuation\">[<\/span>self<span class=\"token punctuation\">.<\/span>dt <span class=\"token operator\">*<\/span> i <span class=\"token keyword\">for<\/span> i <span class=\"token keyword\">in<\/span> <span class=\"token builtin\">range<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#034;path&#034;<\/span><span class=\"token punctuation\">:<\/span> PathPlanner<span class=\"token punctuation\">.<\/span>pathInterpolation<span class=\"token punctuation\">(<\/span>path_seg<span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#034;distance&#034;<\/span><span class=\"token punctuation\">:<\/span> sol<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">:<\/span>n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>tolist<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#034;velocity&#034;<\/span><span class=\"token punctuation\">:<\/span> sol<span class=\"token punctuation\">[<\/span>n<span class=\"token punctuation\">:<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>tolist<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n        <span class=\"token string\">&#034;acceleration&#034;<\/span><span class=\"token punctuation\">:<\/span> sol<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> n<span class=\"token punctuation\">:<\/span><span class=\"token number\">3<\/span> <span class=\"token operator\">*<\/span> n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>tolist<span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token keyword\">return<\/span> velocity_profiles<\/p>\n<p>\u5bf9\u4e8e\u5982\u4e0b\u56fe\u6240\u793a\u7684\u5012\u8f66\u8def\u5f84<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/05\/20250530042619-6839336b1384c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"650\" 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