{"id":79774,"date":"2026-03-03T05:49:27","date_gmt":"2026-03-02T21:49:27","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/79774.html"},"modified":"2026-03-03T05:49:27","modified_gmt":"2026-03-02T21:49:27","slug":"%e3%80%90%e7%bf%bb%e8%af%91%e3%80%91%e9%9d%a2%e5%90%91%e5%b7%a5%e7%a7%91%e5%ad%a6%e7%94%9f%e7%9a%84%e8%bd%a8%e9%81%93%e5%8a%9b%e5%ad%a6-%e7%ac%ac1%e7%ab%a0-%e8%b4%a8%e7%82%b9%e5%8a%a8%e5%8a%9b","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/79774.html","title":{"rendered":"\u3010\u7ffb\u8bd1\u3011\u9762\u5411\u5de5\u79d1\u5b66\u751f\u7684\u8f68\u9053\u529b\u5b66-\u7b2c1\u7ae0-\u8d28\u70b9\u52a8\u529b\u5b66\uff08Part 2\uff09"},"content":{"rendered":"

\u7b2c1\u7ae0-\u8d28\u70b9\u52a8\u529b\u5b66（\u4e2d）<\/h2>\n

1.5 \u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b<\/h3>\n

\u529b\u4e0d\u50cf\u8d28\u91cf\u90a3\u6837\u662f\u4e00\u4e2a\u539f\u59cb\u6982\u5ff5，\u56e0\u4e3a\u5b83\u4e0e\u8fd0\u52a8\u548c\u60ef\u6027\u7684\u6982\u5ff5\u5bc6\u5207\u76f8\u5173\u3002\u4e8b\u5b9e\u4e0a，\u6539\u53d8\u7269\u4f53\u8fd0\u52a8\u7684\u552f\u4e00\u65b9\u6cd5\u662f\u5bf9\u5176\u65bd\u52a0\u529b\u3002\u8fd0\u52a8\u6539\u53d8\u7684\u7a0b\u5ea6\u662f\u529b\u7684\u91cf\u5ea6\u3002\u725b\u987f\u7b2c\u4e8c\u8fd0\u52a8\u5b9a\u5f8b\u91cf\u5316\u4e86\u8fd9\u4e00\u70b9\u3002\u5982\u679c\u8d28\u91cf\u4e3a mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u7269\u4f53\u4e0a\u7684\u5408\u529b\u6216\u51c0\u529b\u662f Fnet\\\\mathbf{F}_{\\\\text{net}}<\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219
\nFnet=ma(1.38)
\n\\\\mathbf {F} _ {\\\\text {net}} = m \\\\mathbf {a} \\\\tag {1.38}
\n<\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>a<\/span><\/span><\/span>(<\/span>1.38<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5728\u8fd9\u4e2a\u65b9\u7a0b\u4e2d，a\\\\mathbf{a}<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span> \u662f\u8d28\u5fc3\u7684\u7edd\u5bf9\u52a0\u901f\u5ea6\u3002\u7edd\u5bf9\u52a0\u901f\u5ea6\u662f\u5728\u76f8\u5bf9\u4e8e\u6052\u661f\u6ca1\u6709\u5e73\u79fb\u6216\u65cb\u8f6c\u52a0\u901f\u5ea6\u7684\u53c2\u8003\u7cfb\u4e2d\u6d4b\u91cf\u7684\u3002\u8fd9\u6837\u7684\u53c2\u8003\u7cfb\u79f0\u4e3a\u7edd\u5bf9\u6216\u60ef\u6027\u53c2\u8003\u7cfb\u3002
\n\u90a3\u4e48，\u529b\u901a\u8fc7\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u4e0e\u8d28\u91cf\u3001\u957f\u5ea6\u548c\u65f6\u95f4\u7684\u539f\u59cb\u6982\u5ff5\u76f8\u5173\u8054\u3002\u529b\u7684\u5355\u4f4d\u9002\u5f53\u5730\u662f\u725b\u987f，\u5373\u8d4b\u4e88 1 kg \u8d28\u91cf\u4ee5 1m\/s21 \\\\mathrm{m\/s^2}<\/span><\/span>1<\/span>m\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u52a0\u901f\u5ea6\u6240\u9700\u7684\u529b\u3002\u56e0\u6b64，\u4e00\u5343\u514b\u7684\u8d28\u91cf\u5728\u5730\u7403\u8868\u9762\u91cd 9.81 \u725b\u987f\u3002\u5343\u514b\u4e0d\u662f\u529b\u7684\u5355\u4f4d\u3002
\n\u5f53\u8d28\u91cf\u7528\u529b\u5355\u4f4d\u8868\u793a\u65f6，\u53ef\u80fd\u4f1a\u4ea7\u751f\u6df7\u6dc6，\u8fd9\u5728\u7f8e\u56fd\u5de5\u7a0b\u5b9e\u8df5\u4e2d\u7ecf\u5e38\u53d1\u751f\u3002\u5728\u901a\u4fd7\u8bf4\u6cd5\u4e2d，\u78c5\u6216\u5428（2000 \u78c5）\u66f4\u53ef\u80fd\u7528\u4e8e\u8868\u793a\u8d28\u91cf\u3002\u78c5\u8d28\u91cf\u6839\u636e\u5343\u514b\u7cbe\u786e\u5b9a\u4e49，\u5982\u8868 A.3 \u6240\u793a\u3002\u7531\u4e8e\u4e00\u78c5\u8d28\u91cf\u5728\u5b58\u5728\u6807\u51c6\u6d77\u5e73\u9762\u91cd\u529b\u52a0\u901f\u5ea6 (g0=9.80665m\/s2)(g_0 = 9.80665 \\\\mathrm{m\/s^2})<\/span><\/span>(<\/span>g<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>9.80665<\/span>m\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u5730\u65b9\u91cd\u4e00\u78c5\u529b，\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u5c06\u78c5\u529b\u4e0e\u725b\u987f\u8054\u7cfb\u8d77\u6765：
\n1lb(\u529b)=0.4536kg\u00d79.807m\/s2=4.448N
\n1 \\\\mathrm {l b} (\\\\text {\u529b}) = 0. 4 5 3 6 \\\\mathrm {k g} \\\\times 9. 8 0 7 \\\\mathrm {m} \/ \\\\mathrm {s} ^ {2} = 4. 4 4 8 \\\\mathrm {N}
\n<\/span><\/span>1<\/span>lb<\/span><\/span>(<\/span>\u529b<\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0.4536<\/span>kg<\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>9.807<\/span>m<\/span>\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>4.448<\/span>N<\/span><\/span><\/span><\/span><\/span><\/span>
\n\u65af\u52d2\u683c (slug) \u662f\u5728\u4e00\u78c5\u529b\u7684\u4f5c\u7528\u4e0b\u4ee5 1ft\/s21 \\\\mathrm{ft\/s^2}<\/span><\/span>1<\/span>ft\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u52a0\u901f\u7684\u7269\u8d28\u7684\u91cf\u3002\u6211\u4eec\u53ef\u4ee5\u518d\u6b21\u4f7f\u7528\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u5c06\u65af\u52d2\u683c\u4e0e\u5343\u514b\u8054\u7cfb\u8d77\u6765\u3002\u6ce8\u610f\u8868 A.3 \u4e2d\u82f1\u5c3a\u548c\u7c73\u4e4b\u95f4\u7684\u5173\u7cfb，\u6211\u4eec\u53d1\u73b0
\n1slug=1lb1ft\/s2=4.448N0.3048m\/s2=14.59kg\u22c5m\/s2m\/s2=14.59kg
\n1 \\\\mathrm {s l u g} = \\\\frac {1 \\\\mathrm {l b}}{1 \\\\mathrm {f t} \/ \\\\mathrm {s} ^ {2}} = \\\\frac {4 . 4 4 8 \\\\mathrm {N}}{0 . 3 0 4 8 \\\\mathrm {m} \/ \\\\mathrm {s} ^ {2}} = 1 4. 5 9 \\\\frac {\\\\mathrm {k g} \\\\cdot \\\\mathrm {m} \/ \\\\mathrm {s} ^ {2}}{\\\\mathrm {m} \/ \\\\mathrm {s} ^ {2}} = 1 4. 5 9 \\\\mathrm {k g}
\n<\/span><\/span>1<\/span>slug<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>ft<\/span><\/span>\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>lb<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>0.3048<\/span>m<\/span>\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>4.448<\/span>N<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>14.59<\/span><\/span><\/span>m<\/span>\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>kg<\/span><\/span><\/span>\u22c5<\/span><\/span>m<\/span>\/<\/span>s<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>14.59<\/span>kg<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4f8b\u9898 1.9
\n\u5728\u4e00\u6b21 NASA \u4efb\u52a1\u4e2d，\u4e9a\u7279\u5170\u8482\u65af\u53f7\u822a\u5929\u98de\u673a\u5728\u5347\u7a7a\u524d\u62a5\u544a\u91cd 239,255 lb\u3002\u5728\u7b2c 18 \u5708\u8f68\u9053\u4e0a，\u9ad8\u5ea6\u7ea6\u4e3a 350km350 \\\\mathrm{km}<\/span><\/span>350<\/span>km<\/span><\/span><\/span><\/span><\/span><\/span>，\u8f68\u9053\u5668\u7684\u91cd\u91cf\u62a5\u544a\u4e3a 236,900 lb\u3002(a) \u4e9a\u7279\u5170\u8482\u65af\u53f7\u5728\u53d1\u5c04\u53f0\u548c\u8f68\u9053\u4e0a\u7684\u8d28\u91cf（\u4ee5\u5343\u514b\u4e3a\u5355\u4f4d）\u662f\u591a\u5c11？(b) \u5982\u679c\u5728\u53d1\u5c04\u548c\u7b2c 18 \u5708\u8f68\u9053\u4e4b\u95f4\u6ca1\u6709\u8d28\u91cf\u635f\u5931，\u4e9a\u7279\u5170\u8482\u65af\u53f7\u7684\u91cd\u91cf（\u4ee5\u78c5\u4e3a\u5355\u4f4d）\u5c06\u662f\u591a\u5c11？
\n\u89e3
\n(a) \u7ed9\u5b9a\u7684\u6570\u636e\u8bf4\u660e\u4e86\u901a\u5e38\u4f7f\u7528\u78c5\u4f5c\u4e3a\u8d28\u91cf\u7684\u5ea6\u91cf\u3002\u7ed9\u51fa\u7684\u201c\u91cd\u91cf\u201d\u5b9e\u9645\u4e0a\u662f\u4ee5\u78c5\u8d28\u91cf\u4e3a\u5355\u4f4d\u7684\u8d28\u91cf\u3002\u56e0\u6b64，\u5728\u53d1\u5c04\u524d
\nm\u53d1\u5c04\u53f0=239,255lb(\u8d28\u91cf)\u00d70.4536kg1lb(\u8d28\u91cf)=108,500kg
\nm _ {\\\\text {\u53d1\u5c04\u53f0}} = 2 3 9, 2 5 5 \\\\mathrm {l b} (\\\\text {\u8d28\u91cf}) \\\\times \\\\frac {0 . 4 5 3 6 \\\\mathrm {k g}}{1 \\\\mathrm {l b} (\\\\text {\u8d28\u91cf})} = \\\\boxed {1 0 8, 5 0 0 \\\\mathrm {k g}}
\n<\/span><\/span>m<\/span><\/span>\u53d1\u5c04\u53f0<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>239<\/span>,<\/span><\/span>255<\/span>lb<\/span><\/span>(<\/span>\u8d28\u91cf<\/span><\/span>)<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>lb<\/span><\/span>(<\/span>\u8d28\u91cf<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.4536<\/span>kg<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>108<\/span>,<\/span><\/span>500<\/span>kg<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5728\u8f68\u9053\u4e0a，
\nm\u8f68\u9053\u00a018=236,900lb(\u8d28\u91cf)\u00d70.4536kg1lb(\u8d28\u91cf)=107,500kg
\nm _ {\\\\text {\u8f68\u9053 18}} = 2 3 6, 9 0 0 \\\\mathrm {l b} (\\\\text {\u8d28\u91cf}) \\\\times \\\\frac {0 . 4 5 3 6 \\\\mathrm {k g}}{1 \\\\mathrm {l b} (\\\\text {\u8d28\u91cf})} = \\\\boxed {1 0 7, 5 0 0 \\\\mathrm {k g}}
\n<\/span><\/span>m<\/span><\/span>\u8f68\u9053<\/span>\u00a018<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>236<\/span>,<\/span><\/span>900<\/span>lb<\/span><\/span>(<\/span>\u8d28\u91cf<\/span><\/span>)<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span>lb<\/span><\/span>(<\/span>\u8d28\u91cf<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>0.4536<\/span>kg<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>107<\/span>,<\/span><\/span>500<\/span>kg<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u8d28\u91cf\u7684\u51cf\u5c11\u662f\u8f68\u9053\u5668\u4e0a\u7684\u8f68\u9053\u673a\u52a8\u548c\u53cd\u4f5c\u7528\u63a7\u5236\u706b\u7bad\u6d88\u8017\u7684\u63a8\u8fdb\u5242\u3002
\n(b) \u7531\u4e8e\u80af\u5c3c\u8fea\u822a\u5929\u4e2d\u5fc3\u7684\u822a\u5929\u98de\u673a\u53d1\u5c04\u53f0\u57fa\u672c\u4e0a\u5904\u4e8e\u6d77\u5e73\u9762，\u4e9a\u7279\u5170\u8482\u65af\u53f7\u5728\u53d1\u5c04\u53f0\u4e0a\u7684\u91cd\u91cf（\u529b）\u5728\u6570\u503c\u4e0a\u7b49\u4e8e\u5176\u8d28\u91cf（\u78c5\u8d28\u91cf）\u3002\u5982\u679c\u6ca1\u6709\u8d28\u91cf\u53d8\u5316，\u6839\u636e\u65b9\u7a0b 1.36，\u5728 350km350 \\\\mathrm{km}<\/span><\/span>350<\/span>km<\/span><\/span><\/span><\/span><\/span><\/span> \u5904\u7684\u91cd\u529b\u5c06\u662f
\nW=239,255lb(\u529b)\u00d7(11+3506378)2=215,000lb(\u529b)
\nW = 2 3 9, 2 5 5 \\\\mathrm {l b} (\\\\text {\u529b}) \\\\times \\\\left(\\\\frac {1}{1 + \\\\frac {3 5 0}{6 3 7 8}}\\\\right) ^ {2} = \\\\boxed {2 1 5, 0 0 0 \\\\mathrm {l b} (\\\\text {\u529b})}
\n<\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>239<\/span>,<\/span><\/span>255<\/span>lb<\/span><\/span>(<\/span>\u529b<\/span><\/span>)<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>6378<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>350<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>215<\/span>,<\/span><\/span>000<\/span>lb<\/span><\/span>(<\/span>\u529b<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u529b F\\\\mathbf{F}<\/span><\/span>F<\/span><\/span><\/span><\/span><\/span> \u5728\u65f6\u95f4\u95f4\u9694\u5185\u7684\u79ef\u5206\u79f0\u4e3a\u529b\u7684\u51b2\u91cf，
\nJ=\u222bt1t2Fdt(1.39)
\n\\\\mathcal {J} = \\\\int_ {t _ {1}} ^ {t _ {2}} \\\\mathbf {F} d t \\\\tag {1.39}
\n<\/span><\/span>J<\/span><\/span>=<\/span><\/span><\/span><\/span>\u222b<\/span><\/span>t<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span>d<\/span>t<\/span><\/span><\/span>(<\/span>1.39<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u51b2\u91cf\u662f\u4e00\u4e2a\u77e2\u91cf\u3002\u4ece\u65b9\u7a0b 1.38 \u53ef\u4ee5\u660e\u663e\u770b\u51fa，\u5982\u679c\u8d28\u91cf\u662f\u6052\u5b9a\u7684，\u90a3\u4e48
\nPnet=\u222bt1t2mdvdtdt=mv2\u2212mv1(1.40)
\n\\\\mathcal {P} _ {\\\\text {net}} = \\\\int_ {t _ {1}} ^ {t _ {2}} m \\\\frac {d \\\\mathbf {v}}{d t} d t = m \\\\mathbf {v} _ {2} – m \\\\mathbf {v} _ {1} \\\\tag {1.40}
\n<\/span><\/span>P<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u222b<\/span><\/span>t<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.40<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5373，\u7269\u4f53\u4e0a\u7684\u51c0\u51b2\u91cf\u4ea7\u751f\u5176\u7ebf\u52a8\u91cf\u7684\u53d8\u5316 m\u0394vm\\\\Delta\\\\mathbf{v}<\/span><\/span>m<\/span>\u0394<\/span>v<\/span><\/span><\/span><\/span><\/span>，\u4f7f\u5f97
\n\u0394v=Pnetm(1.41)
\n\\\\Delta \\\\mathbf {v} = \\\\frac {\\\\mathcal {P} _ {\\\\text {net}}}{m} \\\\tag {1.41}
\n<\/span><\/span>\u0394<\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.41<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5982\u679c Fnet\\\\mathbf{F}_{\\\\text{net}}<\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u6052\u5b9a\u7684，\u90a3\u4e48 Pnet=Fnet\u0394t\\\\boldsymbol{\\\\mathcal{P}}_{\\\\text{net}} = \\\\mathbf{F}_{\\\\text{net}} \\\\Delta t<\/span><\/span>P<\/span><\/span><\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span>，\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u65b9\u7a0b 1.41 \u53d8\u4e3a
\n\u0394v=Fnetm\u0394t(\u5982\u679c\u00a0Fnet\u00a0\u662f\u5e38\u6570)(1.42)
\n\\\\Delta \\\\mathbf {v} = \\\\frac {\\\\mathbf {F} _ {\\\\text {net}}}{m} \\\\Delta t \\\\quad \\\\text {(\u5982\u679c } \\\\mathbf {F} _ {\\\\text {net}} \\\\text { \u662f\u5e38\u6570)} \\\\tag {1.42}
\n<\/span><\/span>\u0394<\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span>(<\/span>\u5982\u679c<\/span>\u00a0<\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0<\/span>\u662f\u5e38\u6570<\/span>)<\/span><\/span><\/span><\/span>(<\/span>1.42<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u8ba9\u6211\u4eec\u901a\u8fc7\u5f15\u5165\u89d2\u52a8\u91cf\u7684\u6982\u5ff5\u6765\u7ed3\u675f\u672c\u8282\u3002\u56fe 1.13 \u4e2d\u51c0\u529b\u5173\u4e8e oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span> \u7684\u529b\u77e9\u662f
\nMOnet=r\u00d7Fnet
\n\\\\mathbf {M} _ {O \\\\text {net}} = \\\\mathbf {r} \\\\times \\\\mathbf {F} _ {\\\\text {net}}
\n<\/span><\/span>M<\/span><\/span>O<\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>F<\/span><\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4ee3\u5165\u65b9\u7a0b 1.38 \u5f97\u51fa
\nMOnet=r\u00d7ma=r\u00d7mdvdt(1.43)
\n\\\\mathbf {M} _ {O \\\\text {net}} = \\\\mathbf {r} \\\\times m \\\\mathbf {a} = \\\\mathbf {r} \\\\times m \\\\frac {d \\\\mathbf {v}}{d t} \\\\tag {1.43}
\n<\/span><\/span>M<\/span><\/span>O<\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>a<\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.43<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4f46\u662f，\u8bb0\u4f4f\u8d28\u91cf\u662f\u6052\u5b9a\u7684，
\nr\u00d7mdvdt=ddt(r\u00d7mv)\u2212(drdt\u00d7mv)=ddt(r\u00d7mv)\u2212(v\u00d7mv)
\n\\\\mathbf {r} \\\\times m \\\\frac {d \\\\mathbf {v}}{d t} = \\\\frac {d}{d t} (\\\\mathbf {r} \\\\times m \\\\mathbf {v}) – \\\\left(\\\\frac {d \\\\mathbf {r}}{d t} \\\\times m \\\\mathbf {v}\\\\right) = \\\\frac {d}{d t} (\\\\mathbf {r} \\\\times m \\\\mathbf {v}) – (\\\\mathbf {v} \\\\times m \\\\mathbf {v})
\n<\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>r<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>m<\/span>v<\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>v<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>
\n\u7531\u4e8e v\u00d7mv=m(v\u00d7v)=0\\\\mathbf{v} \\\\times m\\\\mathbf{v} = m(\\\\mathbf{v} \\\\times \\\\mathbf{v}) = \\\\mathbf{0}<\/span><\/span>v<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>(<\/span>v<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>v<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u56e0\u6b64\u65b9\u7a0b 1.43 \u53ef\u4ee5\u5199\u6210
\nMOnet=dHOdt(1.44)
\n\\\\mathbf {M} _ {O \\\\text {net}} = \\\\frac {d \\\\mathbf {H} _ {O}}{d t} \\\\tag {1.44}
\n<\/span><\/span>M<\/span><\/span>O<\/span>net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>H<\/span><\/span>O<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.44<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d HO\\\\mathbf{H}_O<\/span><\/span>H<\/span><\/span>O<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5173\u4e8e oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span> \u7684\u89d2\u52a8\u91cf，
\nHO=r\u00d7mv(1.45)
\n\\\\mathbf {H} _ {O} = \\\\mathbf {r} \\\\times m \\\\mathbf {v} \\\\tag {1.45}
\n<\/span><\/span>H<\/span><\/span>O<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span><\/span>(<\/span>1.45<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\"1.13\"<\/p>\n

\n \u56fe 1.13<\/b> \u8d28\u70b9\u7684\u7edd\u5bf9\u52a0\u901f\u5ea6\u5728\u5408\u529b\u7684\u65b9\u5411\u4e0a\u3002\n<\/p>\n

\u56e0\u6b64，\u5c31\u50cf\u8d28\u70b9\u4e0a\u7684\u51c0\u529b\u6539\u53d8\u5176\u7ebf\u52a8\u91cf mvm\\\\mathbf{v}<\/span><\/span>m<\/span>v<\/span><\/span><\/span><\/span><\/span> \u4e00\u6837，\u8be5\u529b\u5173\u4e8e\u56fa\u5b9a\u70b9\u7684\u529b\u77e9\u6539\u53d8\u5176\u5173\u4e8e\u8be5\u70b9\u7684\u7ebf\u52a8\u91cf\u77e9\u3002\u5bf9\u65b9\u7a0b 1.44 \u5bf9\u65f6\u95f4\u79ef\u5206\u5f97\u51fa
\n\u222bt1t2MO\u00a0netdt=HO2\u2212HO1(1.46)
\n\\\\int_ {t _ {1}} ^ {t _ {2}} \\\\mathbf {M} _ {\\\\text {O net}} d t = \\\\mathbf {H} _ {O 2} – \\\\mathbf {H} _ {O 1} \\\\tag {1.46}
\n<\/span><\/span>\u222b<\/span><\/span>t<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>M<\/span><\/span>O\u00a0net<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span><\/span>O<\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>H<\/span><\/span>O<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.46<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5de6\u8fb9\u7684\u79ef\u5206\u662f\u51c0\u89d2\u51b2\u91cf\u3002\u8fd9\u4e2a\u89d2\u51b2\u91cf-\u52a8\u91cf\u65b9\u7a0b\u662f\u65b9\u7a0b 1.40 \u4e2d\u7ed9\u51fa\u7684\u7ebf\u6027\u51b2\u91cf-\u52a8\u91cf\u5173\u7cfb\u7684\u65cb\u8f6c\u7c7b\u6bd4\u3002<\/p>\n

\u4f8b\u9898 1.10
\n\u8d28\u91cf\u4e3a mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u8d28\u70b9\u901a\u8fc7\u957f\u5ea6\u4e3a ll<\/span><\/span>l<\/span><\/span><\/span><\/span><\/span> \u7684\u4e0d\u53ef\u4f38\u957f\u7684\u7ef3\u5b50\u8fde\u63a5\u5230\u70b9 oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>（\u56fe 1.14）\u3002\u6700\u521d\u5f53 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4ee5\u901f\u5ea6 v0v_0<\/span><\/span>v<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5411\u5de6\u79fb\u52a8\u5230\u6240\u793a\u4f4d\u7f6e\u65f6，\u7ef3\u5b50\u662f\u677e\u5f1b\u7684\u3002\u8ba1\u7b97 (a) \u7ef3\u5b50\u62c9\u7d27\u540e mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u901f\u5ea6，\u4ee5\u53ca (b) \u5728\u6539\u53d8\u8d28\u70b9\u8fd0\u52a8\u65b9\u5411\u6240\u9700\u7684\u5fae\u5c0f\u65f6\u95f4\u95f4\u9694 \u0394t\\\\Delta t<\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span> \u5185\u7ef3\u5b50\u4e2d\u7684\u5e73\u5747\u529b\u3002
\n\u89e3
\n(a) \u6700\u521d，\u8d28\u70b9\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u662f
\nr1=ci^+dj^v1=\u2212voi^
\n\\\\mathbf {r} _ {1} = c \\\\hat {\\\\mathbf {i}} + d \\\\hat {\\\\mathbf {j}} \\\\quad \\\\mathbf {v} _ {1} = – v _ {o} \\\\hat {\\\\mathbf {i}}
\n<\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>c<\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5173\u4e8e oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span> \u7684\u89d2\u52a8\u91cf\u662f
\nH1=r1\u00d7mv1=\u2223i^j^k^cd0\u2212mvo00\u2223=mvodk^(a)
\n\\\\mathbf {H} _ {1} = \\\\mathbf {r} _ {1} \\\\times m \\\\mathbf {v} _ {1} = \\\\left| \\\\begin{array}{c c c} \\\\hat {\\\\mathbf {i}} & \\\\hat {\\\\mathbf {j}} & \\\\hat {\\\\mathbf {k}} \\\\\\\\ c & d & 0 \\\\\\\\ – m v _ {o} & 0 & 0 \\\\end{array} \\\\right| = m v _ {o} d \\\\hat {\\\\mathbf {k}} \\\\tag {a}
\n<\/span><\/span>H<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span>\u2212<\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>a<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u7ef3\u5b50\u62c9\u7d27\u540e
\nr2=\u2212l2\u2212d2i^+dj^v2=vxi^+vyj^(b)
\n\\\\mathbf {r} _ {2} = – \\\\sqrt {l ^ {2} – d ^ {2}} \\\\hat {\\\\mathbf {i}} + d \\\\hat {\\\\mathbf {j}} \\\\quad \\\\mathbf {v} _ {2} = v _ {x} \\\\hat {\\\\mathbf {i}} + v _ {y} \\\\hat {\\\\mathbf {j}} \\\\tag {b}
\n<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>b<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\"1.14\"<\/p>\n

\n \u56fe 1.14<\/b> \u901a\u8fc7\u4e0d\u53ef\u4f38\u957f\u7684\u7ef3\u5b50\u8fde\u63a5\u5230 $o$ \u7684\u8d28\u70b9\u3002\n<\/p>\n

\u89d2\u52a8\u91cf\u662f
\nH2=r2\u00d7mv2=\u2223i^j^k^\u2212l2\u2212d2d0vxvy0\u2223=(\u2212mvxd\u2212mvyl2\u2212d2)k^(c)
\n\\\\mathbf {H} _ {2} = \\\\mathbf {r} _ {2} \\\\times m \\\\mathbf {v} _ {2} = \\\\left| \\\\begin{array}{c c c} \\\\hat {\\\\mathbf {i}} & \\\\hat {\\\\mathbf {j}} & \\\\hat {\\\\mathbf {k}} \\\\\\\\ – \\\\sqrt {l ^ {2} – d ^ {2}} & d & 0 \\\\\\\\ v _ {x} & v _ {y} & 0 \\\\end{array} \\\\right| = (- m v _ {x} d – m v _ {y} \\\\sqrt {l ^ {2} – d ^ {2}}) \\\\hat {\\\\mathbf {k}} \\\\tag {c}
\n<\/span><\/span>H<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>m<\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>c<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u6700\u521d\u677e\u5f1b\u7684\u7ef3\u5b50\u5bf9 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u65bd\u52a0\u7684\u529b\u4e3a\u96f6\u3002\u5f53\u7ef3\u5b50\u62c9\u7d27\u65f6，\u65bd\u52a0\u5728 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e0a\u7684\u529b\u901a\u8fc7 oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u3002\u56e0\u6b64，\u51c0\u529b\u5bf9 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u5173\u4e8e oo<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span> \u7684\u529b\u77e9\u4fdd\u6301\u4e3a\u96f6\u3002\u6839\u636e\u65b9\u7a0b 1.46，
\nH2=H1
\n\\\\mathbf {H} _ {2} = \\\\mathbf {H} _ {1}
\n<\/span><\/span>H<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4ee3\u5165 (a) \u548c \u00a9，\u5f97\u51fa
\nvxd+l2\u2212d2vy=\u2212vod(d)
\nv _ {x} d + \\\\sqrt {l ^ {2} – d ^ {2}} v _ {y} = – v _ {o} d \\\\tag {d}
\n<\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span>(<\/span>d<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u7ef3\u5b50\u662f\u4e0d\u53ef\u4f38\u957f\u7684，\u6240\u4ee5 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u6cbf\u7ef3\u5b50\u7684\u901f\u5ea6\u5206\u91cf\u5fc5\u987b\u4e3a\u96f6：
\nv2\u22c5r2=0
\n\\\\mathbf {v} _ {2} \\\\cdot \\\\mathbf {r} _ {2} = 0
\n<\/span><\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4ee3\u5165 (b) \u4e2d\u7684 v2\\\\mathbf{v}_2<\/span><\/span>v<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c r2\\\\mathbf{r}_2<\/span><\/span>r<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5e76\u89e3\u51fa vyv_y<\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6211\u4eec\u5f97\u5230
\nvy=vxl2d2\u22121(e)
\nv _ {y} = v _ {x} \\\\sqrt {\\\\frac {l ^ {2}}{d ^ {2}} – 1} \\\\tag {e}
\n<\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>e<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u89e3 (d) \u548c (e) \u6c42 vxv_x<\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c vyv_y<\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bfc\u81f4
\nvx=\u2212d2l2vovy=\u22121\u2212d2l2dlvo(f)
\nv _ {x} = – \\\\frac {d ^ {2}}{l ^ {2}} v _ {o} \\\\quad v _ {y} = – \\\\sqrt {1 – \\\\frac {d ^ {2}}{l ^ {2}}} \\\\frac {d}{l} v _ {o} \\\\tag {f}
\n<\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>f<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u56e0\u6b64，\u7ef3\u5b50\u62c9\u7d27\u540e\u7684\u901f\u5ea6 v=vx2+vy2v = \\\\sqrt{v_x^2 + v_y^2}<\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>x<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>v<\/span><\/span>y<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f
\nv=dlvo
\n\\\\boxed {v = \\\\frac {d}{l} v _ {o}}
\n<\/span><\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n(b) \u4ece\u65b9\u7a0b 1.40，\u5728\u7ef3\u5b50\u62c9\u7d27\u6240\u9700\u7684\u65f6\u95f4\u5185\u5bf9 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u7684\u51b2\u91cf\u662f
\nP=m(v2\u2212v1)=m[(\u2212d2l2voi^\u22121\u2212d2l2dlvoj^)\u2212(\u2212voi^)]=(1\u2212d2l2)mvoi^\u22121\u2212d2l2dlmvoj^
\n\\\\mathcal {P} = m \\\\left(\\\\mathbf {v} _ {2 -} \\\\mathbf {v} _ {1}\\\\right) = m \\\\left[ \\\\left(- \\\\frac {d ^ {2}}{l ^ {2}} v _ {o} \\\\hat {\\\\mathbf {i}} – \\\\sqrt {1 – \\\\frac {d ^ {2}}{l ^ {2}}} \\\\frac {d}{l} v _ {o} \\\\hat {\\\\mathbf {j}}\\\\right) – (- v _ {o} \\\\hat {\\\\mathbf {i}}) \\\\right] = \\\\left(1 – \\\\frac {d ^ {2}}{l ^ {2}}\\\\right) m v _ {o} \\\\hat {\\\\mathbf {i}} – \\\\sqrt {1 – \\\\frac {d ^ {2}}{l ^ {2}}} \\\\frac {d}{l} m v _ {o} \\\\hat {\\\\mathbf {j}}
\n<\/span><\/span>P<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span>(<\/span>v<\/span><\/span>2<\/span>\u2212<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span><\/span>[<\/span><\/span>(<\/span><\/span>\u2212<\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>(<\/span>\u2212<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u8fd9\u4e2a\u6cbf\u7ef3\u5b50\u65b9\u5411\u7684\u51b2\u91cf\u7684\u5927\u5c0f\u662f
\nI=1\u2212d2l2mvo
\n\\\\mathcal {I} = \\\\sqrt {1 – \\\\frac {d ^ {2}}{l ^ {2}}} m v _ {o}
\n<\/span><\/span>I<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u56e0\u6b64，\u5728\u6539\u53d8\u901f\u5ea6\u77e2\u91cf\u65b9\u5411\u6240\u9700\u7684\u5fae\u5c0f\u65f6\u95f4\u95f4\u9694 \u0394t\\\\Delta t<\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span> \u5185，\u7ef3\u5b50\u4e2d\u7684\u5e73\u5747\u529b\u7ed3\u679c\u662f
\nFavg=I\u0394t=1\u2212d2l2mvo\u0394t
\nF _ {a v g} = \\\\frac {\\\\mathcal {I}}{\\\\Delta t} = \\\\boxed {\\\\sqrt {1 – \\\\frac {d ^ {2}}{l ^ {2}}} \\\\frac {m v _ {o}}{\\\\Delta t}}
\n<\/span><\/span>F<\/span><\/span>a<\/span>vg<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>I<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span>o<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

1.6 \u8fd0\u52a8\u77e2\u91cf\u7684\u5bfc\u6570<\/h3>\n

\u56fe 1.15(a) \u663e\u793a\u4e86\u4e00\u4e2a\u5d4c\u5165\u5728\u521a\u4f53 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u77e2\u91cf A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>，\u8be5\u521a\u4f53\u76f8\u5bf9\u4e8e\u60ef\u6027\u53c2\u8003\u7cfb（\u76f8\u5bf9\u4e8e\u6052\u661f\u56fa\u5b9a\u7684\u521a\u6027\u7b1b\u5361\u5c14\u5750\u6807\u7cfb）\u8fd0\u52a8\u3002A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u5927\u5c0f\u662f\u56fa\u5b9a\u7684\u3002\u7269\u4f53 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u663e\u793a\u5728\u4e24\u4e2a\u65f6\u95f4\u70b9，\u76f8\u9694\u5fae\u5206\u65f6\u95f4\u95f4\u9694 dtdt<\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u65f6\u95f4 t+dtt + dt<\/span><\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span>，\u77e2\u91cf A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u65b9\u5411\u4e0e\u65f6\u95f4 tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u65f6\u7565\u6709\u4e0d\u540c，\u4f46\u5176\u5927\u5c0f\u76f8\u540c\u3002\u6839\u636e 18 \u4e16\u7eaa\u591a\u4ea7\u7684\u745e\u58eb\u6570\u5b66\u5bb6\u83b1\u6602\u54c8\u5fb7\u00b7\u6b27\u62c9 (1707 \u2013 1783) \u7684\u4f17\u591a\u5b9a\u7406\u4e4b\u4e00，\u5b58\u5728\u4e00\u4e2a\u552f\u4e00\u7684\u65cb\u8f6c\u8f74，\u7269\u4f53 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4ee5\u53ca\u56e0\u6b64 A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5728\u5fae\u5206\u65f6\u95f4\u95f4\u9694\u5185\u7ed5\u8be5\u8f74\u65cb\u8f6c\u3002\u5982\u679c\u6211\u4eec\u5c06\u4e24\u4e2a\u77e2\u91cf A(t)\\\\mathbf{A}(t)<\/span><\/span>A<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c A(t+dt)\\\\mathbf{A}(t + dt)<\/span><\/span>A<\/span>(<\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u79fb\u52a8\u5230\u65cb\u8f6c\u8f74\u4e0a\u7684\u540c\u4e00\u70b9，\u4f7f\u5b83\u4eec\u5c3e\u5bf9\u5c3e\u5982\u56fe 1.15(b) \u6240\u793a，\u6211\u4eec\u53ef\u4ee5\u8bc4\u4f30\u7531\u65e0\u9650\u5c0f\u65cb\u8f6c\u5f15\u8d77\u7684\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02 dAd\\\\mathbf{A}<\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span><\/span>\u3002\u8bf7\u8bb0\u4f4f，\u5c06\u77e2\u91cf\u79fb\u52a8\u5230\u5e73\u884c\u7ebf\u4e0d\u4f1a\u6539\u53d8\u77e2\u91cf\u3002\u7269\u4f53 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u65cb\u8f6c\u662f\u5728\u5782\u76f4\u4e8e\u77ac\u65f6\u65cb\u8f6c\u8f74\u7684\u5e73\u9762\u5185\u6d4b\u91cf\u7684\u3002\u65cb\u8f6c\u91cf\u662f\u5782\u76f4\u4e8e\u65cb\u8f6c\u8f74\u7684\u7ebf\u5143\u7d20\u5728\u65f6\u95f4\u95f4\u9694 dtdt<\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span> \u5185\u8f6c\u8fc7\u7684\u89d2\u5ea6 d\u03b8d\\\\theta<\/span><\/span>d<\/span>\u03b8<\/span><\/span><\/span><\/span><\/span>\u3002\u5728\u56fe 1.15(b) \u4e2d，\u8be5\u7ebf\u5143\u7d20\u662f A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5782\u76f4\u4e8e\u65cb\u8f6c\u8f74\u7684\u5206\u91cf\u3002\u6211\u4eec\u53ef\u4ee5\u5c06 A(t)\\\\mathbf{A}(t)<\/span><\/span>A<\/span>(<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u548c A(t+dt)\\\\mathbf{A}(t + dt)<\/span><\/span>A<\/span>(<\/span>t<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u7684\u5dee\u5f02 dAd\\\\mathbf{A}<\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u4e3a
\ndA=[(\u2225A\u2225\u22c5sin\u2061\u03d5)d\u03b8]\u23dedA\u00a0\u7684\u5927\u5c0fn^(1.47)
\nd \\\\mathbf {A} = \\\\overbrace {\\\\left[ \\\\left(\\\\left\\\\| \\\\mathbf {A} \\\\right\\\\| \\\\cdot \\\\sin \\\\phi\\\\right) d \\\\theta \\\\right]} ^ {d \\\\mathbf {A} \\\\text { \u7684\u5927\u5c0f}} \\\\hat {\\\\mathbf {n}} \\\\tag {1.47}
\n<\/span><\/span>d<\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>(<\/span>\u2225<\/span>A<\/span>\u2225<\/span><\/span><\/span>\u22c5<\/span><\/span>sin<\/span><\/span>\u03d5<\/span>)<\/span><\/span><\/span>d<\/span>\u03b8<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span>\u00a0<\/span>\u7684\u5927\u5c0f<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.47<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\n<\/tr>\n\n\n\n
\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/td>\n\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/td>\n<\/tr>\n
(a)<\/td>\n(b)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\n \u56fe 1.15<\/b> \u521a\u4f53\u7684\u4f4d\u79fb\u3002\n<\/p>\n

\u5176\u4e2d n^\\\\hat{\\\\mathbf{n}}<\/span><\/span><\/span>n<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u7531 A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u548c\u65cb\u8f6c\u8f74\u5b9a\u4e49\u7684\u5e73\u9762\u7684\u5355\u4f4d\u6cd5\u7ebf，\u5b83\u6307\u5411\u65cb\u8f6c\u65b9\u5411\u3002\u89d2\u5ea6 \u03d5\\\\phi<\/span><\/span>\u03d5<\/span><\/span><\/span><\/span><\/span> \u662f A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5bf9\u65cb\u8f6c\u8f74\u7684\u503e\u89d2\u3002\u6839\u636e\u5b9a\u4e49，
\nd\u03b8=\u2225\u03c9\u2225dt(1.48)
\nd \\\\theta = \\\\| \\\\boldsymbol {\\\\omega} \\\\| d t \\\\tag {1.48}
\n<\/span><\/span>d<\/span>\u03b8<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2225<\/span>\u03c9<\/span><\/span><\/span>\u2225<\/span>d<\/span>t<\/span><\/span><\/span>(<\/span>1.48<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u89d2\u901f\u5ea6\u77e2\u91cf，\u5b83\u6cbf\u77ac\u65f6\u65cb\u8f6c\u8f74\u6307\u5411，\u5176\u65b9\u5411\u7531\u53f3\u624b\u5b9a\u5219\u7ed9\u51fa\u3002\u5373，\u53f3\u624b\u63e1\u4f4f\u65cb\u8f6c\u8f74，\u624b\u6307\u6307\u5411 d\u03b8d\\\\theta<\/span><\/span>d<\/span>\u03b8<\/span><\/span><\/span><\/span><\/span> \u7684\u65b9\u5411，\u62c7\u6307\u5b9a\u4e49 \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u65b9\u5411\u3002\u8fd9\u5728\u56fe 1.15(b) \u4e2d\u5f88\u660e\u663e\u3002\u9700\u8981\u6307\u51fa\u7684\u662f，\u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u65f6\u95f4\u5bfc\u6570\u662f\u89d2\u52a0\u901f\u5ea6，\u901a\u5e38\u7528\u7b26\u53f7 \u03b1\\\\boldsymbol{\\\\alpha}<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u3002\u56e0\u6b64，
\n\u03b1=d\u03c9dt(1.49)
\n\\\\boldsymbol{\\\\alpha} = \\\\frac {d \\\\boldsymbol{\\\\omega}}{d t} \\\\tag {1.49}
\n<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.49<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5c06\u65b9\u7a0b 1.48 \u4ee3\u5165\u65b9\u7a0b 1.47，\u6211\u4eec\u5f97\u5230
\ndA=\u2225A\u2225\u22c5sin\u2061\u03d5\u22c5\u2225\u03c9\u2225dt\u22c5n^=(\u2225\u03c9\u2225\u22c5\u2225A\u2225\u22c5sin\u2061\u03d5)n^dt(1.50)
\nd \\\\mathbf {A} = \\\\| \\\\mathbf {A} \\\\| \\\\cdot \\\\sin \\\\phi \\\\cdot \\\\| \\\\boldsymbol {\\\\omega} \\\\| d t \\\\cdot \\\\hat {\\\\mathbf {n}} = \\\\left(\\\\| \\\\boldsymbol {\\\\omega} \\\\| \\\\cdot \\\\| \\\\mathbf {A} \\\\| \\\\cdot \\\\sin \\\\phi\\\\right) \\\\hat {\\\\mathbf {n}} d t \\\\tag {1.50}
\n<\/span><\/span>d<\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2225<\/span>A<\/span>\u2225<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>sin<\/span><\/span>\u03d5<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u2225<\/span>\u03c9<\/span><\/span><\/span>\u2225<\/span>d<\/span>t<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>\u2225<\/span>\u03c9<\/span><\/span><\/span>\u2225<\/span><\/span>\u22c5<\/span><\/span>\u2225<\/span>A<\/span>\u2225<\/span><\/span>\u22c5<\/span><\/span>sin<\/span><\/span>\u03d5<\/span>)<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span>(<\/span>1.50<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u6839\u636e\u53c9\u79ef\u7684\u5b9a\u4e49，\u03c9\u00d7A\\\\boldsymbol{\\\\omega} \\\\times \\\\mathbf{A}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u662f \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5927\u5c0f\u3001A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u5927\u5c0f\u3001\u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u5939\u89d2\u7684\u6b63\u5f26\u4ee5\u53ca\u5782\u76f4\u4e8e \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u5e73\u9762\u7684\u5355\u4f4d\u6cd5\u7ebf\u7684\u4e58\u79ef，\u5728\u65cb\u8f6c\u65b9\u5411\u4e0a\u3002\u5373，
\n\u03c9\u00d7A=\u2225\u03c9\u2225\u22c5\u2225A\u2225\u22c5sin\u2061\u03d5\u22c5n^(1.51)
\n\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A} = \\\\| \\\\boldsymbol {\\\\omega} \\\\| \\\\cdot \\\\| \\\\mathbf {A} \\\\| \\\\cdot \\\\sin \\\\phi \\\\cdot \\\\hat {\\\\mathbf {n}} \\\\tag {1.51}
\n<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2225<\/span>\u03c9<\/span><\/span><\/span>\u2225<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u2225<\/span>A<\/span>\u2225<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>sin<\/span><\/span>\u03d5<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span>n<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.51<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5c06\u65b9\u7a0b 1.51 \u4ee3\u5165\u65b9\u7a0b 1.50 \u5f97\u51fa
\ndA=\u03c9\u00d7Adt
\nd \\\\mathbf {A} = \\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A} d t
\n<\/span><\/span>d<\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span>
\n\u9664\u4ee5 dtdt<\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span>，\u6211\u4eec\u6700\u7ec8\u83b7\u5f97
\ndAdt=\u03c9\u00d7A(\u5982\u679cddt\u2225A\u2225=0)(1.52)
\n\\\\boxed {\\\\frac {d \\\\mathbf {A}}{d t} = \\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}} \\\\quad \\\\left(\\\\text {\u5982\u679c} \\\\frac {d}{d t} \\\\| \\\\mathbf {A} \\\\| = 0\\\\right) \\\\tag {1.52}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u5982\u679c<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2225<\/span>A<\/span>\u2225<\/span><\/span>=<\/span><\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span>(<\/span>1.52<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u65b9\u7a0b 1.52 \u662f\u6211\u4eec\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u5927\u5c0f\u6052\u5b9a\u7684\u65cb\u8f6c\u77e2\u91cf\u7684\u65f6\u95f4\u5bfc\u6570\u7684\u516c\u5f0f\u3002<\/p>\n

\u4f8b\u9898 1.11
\n\u8ba1\u7b97\u5927\u5c0f\u6052\u5b9a\u7684\u77e2\u91cf A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u4e8c\u9636\u65f6\u95f4\u5bfc\u6570，\u5c06\u7ed3\u679c\u7528 \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ca\u5176\u5bfc\u6570\u548c A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u3002
\n\u89e3
\n\u5bf9\u65b9\u7a0b 1.52 \u5bf9\u65f6\u95f4\u6c42\u5bfc，\u6211\u4eec\u5f97\u5230
\nd2Adt2=ddtdAdt=ddt(\u03c9\u00d7A)=d\u03c9dt\u00d7A+\u03c9\u00d7dAdt
\n\\\\frac {d ^ {2} \\\\mathbf {A}}{d t ^ {2}} = \\\\frac {d}{d t} \\\\frac {d \\\\mathbf {A}}{d t} = \\\\frac {d}{d t} (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) = \\\\frac {d \\\\boldsymbol {\\\\omega}}{d t} \\\\times \\\\mathbf {A} + \\\\boldsymbol {\\\\omega} \\\\times \\\\frac {d \\\\mathbf {A}}{d t}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>A<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4f7f\u7528\u65b9\u7a0b 1.49 \u548c 1.52，\u8fd9\u53ef\u4ee5\u5199\u6210
\nd2Adt2=\u03b1\u00d7A+\u03c9\u00d7(\u03c9\u00d7A)(1.53)
\n\\\\boxed {\\\\frac {d ^ {2} \\\\mathbf {A}}{d t ^ {2}} = \\\\boldsymbol {\\\\alpha} \\\\times \\\\mathbf {A} + \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A})} \\\\tag {1.53}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.53<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u4f8b\u9898 1.12
\n\u8ba1\u7b97\u5927\u5c0f\u6052\u5b9a\u7684\u77e2\u91cf A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u4e09\u9636\u5bfc\u6570，\u5c06\u7ed3\u679c\u7528 \u03c9\\\\boldsymbol{\\\\omega}<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ca\u5176\u5bfc\u6570\u548c A\\\\mathbf{A}<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u3002
\n\u89e3
\nd3Adt3=ddtd2Adt2=ddt[\u03b1\u00d7A+\u03c9\u00d7(\u03c9\u00d7A)]=ddt(\u03b1\u00d7A)+ddt[\u03c9\u00d7(\u03c9\u00d7A)]=(d\u03b1dt\u00d7A+\u03b1\u00d7dAdt)+[d\u03c9dt\u00d7(\u03c9\u00d7A)+\u03c9\u00d7ddt(\u03c9\u00d7A)]=[d\u03b1dt\u00d7A+\u03b1\u00d7(\u03c9\u00d7A)]+[\u03b1\u00d7(\u03c9\u00d7A)+\u03c9\u00d7(d\u03c9dt\u00d7A+\u03c9\u00d7dAdt)]=[d\u03b1dt\u00d7A+\u03b1\u00d7(\u03c9\u00d7A)]+{\u03b1\u00d7(\u03c9\u00d7A)+\u03c9\u00d7[\u03b1\u00d7A+\u03c9\u00d7(\u03c9\u00d7A)]}=d\u03b1dt\u00d7A+\u03b1\u00d7(\u03c9\u00d7A)+\u03b1\u00d7(\u03c9\u00d7A)+\u03c9\u00d7(\u03b1\u00d7A)+\u03c9\u00d7[\u03c9\u00d7(\u03c9\u00d7A)]=d\u03b1dt\u00d7A+2\u03b1\u00d7(\u03c9\u00d7A)+\u03c9\u00d7(\u03b1\u00d7A)+\u03c9\u00d7[\u03c9\u00d7(\u03c9\u00d7A)]
\n\\\\begin{array}{l} \\\\frac {d ^ {3} \\\\mathbf {A}}{d t ^ {3}} = \\\\frac {d}{d t} \\\\frac {d ^ {2} \\\\mathbf {A}}{d t ^ {2}} = \\\\frac {d}{d t} [ \\\\boldsymbol {\\\\alpha} \\\\times \\\\mathbf {A} + \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) ] \\\\\\\\ = \\\\frac {d}{d t} (\\\\boldsymbol {\\\\alpha} \\\\times \\\\mathbf {A}) + \\\\frac {d}{d t} [ \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) ] \\\\\\\\ = \\\\left(\\\\frac {d \\\\mathbf {\\\\alpha}}{d t} \\\\times \\\\mathbf {A} + \\\\mathbf {\\\\alpha} \\\\times \\\\frac {d \\\\mathbf {A}}{d t}\\\\right) + \\\\left[ \\\\frac {d \\\\boldsymbol {\\\\omega}}{d t} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) + \\\\boldsymbol {\\\\omega} \\\\times \\\\frac {d}{d t} (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) \\\\right] \\\\\\\\ = \\\\left[ \\\\frac {d \\\\mathbf {\\\\alpha}}{d t} \\\\times \\\\mathbf {A} + \\\\mathbf {\\\\alpha} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) \\\\right] + \\\\left[ \\\\mathbf {\\\\alpha} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) + \\\\boldsymbol {\\\\omega} \\\\times \\\\left(\\\\frac {d \\\\boldsymbol {\\\\omega}}{d t} \\\\times \\\\mathbf {A} + \\\\boldsymbol {\\\\omega} \\\\times \\\\frac {d \\\\mathbf {A}}{d t}\\\\right) \\\\right] \\\\\\\\ = \\\\left[ \\\\frac {d \\\\alpha}{d t} \\\\times \\\\mathbf {A} + \\\\alpha \\\\times (\\\\omega \\\\times \\\\mathbf {A}) \\\\right] + \\\\left\\\\{\\\\alpha \\\\times (\\\\omega \\\\times \\\\mathbf {A}) + \\\\omega \\\\times [ \\\\alpha \\\\times \\\\mathbf {A} + \\\\omega \\\\times (\\\\omega \\\\times \\\\mathbf {A}) ] \\\\right\\\\} \\\\\\\\ = \\\\frac {d \\\\alpha}{d t} \\\\times \\\\mathbf {A} + \\\\alpha \\\\times (\\\\omega \\\\times \\\\mathbf {A}) + \\\\alpha \\\\times (\\\\omega \\\\times \\\\mathbf {A}) + \\\\omega \\\\times (\\\\alpha \\\\times \\\\mathbf {A}) + \\\\omega \\\\times [ \\\\omega \\\\times (\\\\omega \\\\times \\\\mathbf {A}) ] \\\\\\\\ = \\\\frac {d \\\\boldsymbol {\\\\alpha}}{d t} \\\\times \\\\mathbf {A} + 2 \\\\boldsymbol {\\\\alpha} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) + \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\alpha} \\\\times \\\\mathbf {A}) + \\\\boldsymbol {\\\\omega} \\\\times [ \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) ] \\\\\\\\ \\\\end{array}
\n<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span><\/span><\/span><\/span>=<\/span><\/span>(<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>+<\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span>]<\/span><\/span><\/span><\/span>+<\/span><\/span>[<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span>]<\/span><\/span><\/span><\/span>+<\/span><\/span>{<\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>[<\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span>}<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>[<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>2<\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>[<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\nd3Adt3=d\u03b1dt\u00d7A+2\u03b1\u00d7(\u03c9\u00d7A)+\u03c9\u00d7[\u03b1\u00d7A+\u03c9\u00d7(\u03c9\u00d7A)]
\n\\\\boxed {\\\\frac {d ^ {3} \\\\mathbf {A}}{d t ^ {3}} = \\\\frac {d \\\\alpha}{d t} \\\\times \\\\mathbf {A} + 2 \\\\alpha \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) + \\\\boldsymbol {\\\\omega} \\\\times [ \\\\boldsymbol {\\\\alpha} \\\\times \\\\mathbf {A} + \\\\boldsymbol {\\\\omega} \\\\times (\\\\boldsymbol {\\\\omega} \\\\times \\\\mathbf {A}) ]}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03b1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>2<\/span>\u03b1<\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>[<\/span>\u03b1<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span><\/span>+<\/span><\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span>\u03c9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>A<\/span>)]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8bbe XYZ \u4e3a\u521a\u6027\u60ef\u6027\u53c2\u8003\u7cfb，xyz \u4e3a\u521a\u6027\u79fb\u52a8\u53c2\u8003\u7cfb，\u5982\u56fe 1.16 \u6240\u793a\u3002\u79fb\u52a8\u7cfb\u53ef\u4ee5\u81ea\u884c\u81ea\u7531\u79fb\u52a8（\u5e73\u79fb\u548c\u65cb\u8f6c），\u4e5f\u53ef\u4ee5\u9644\u7740\u5728\u7269\u7406\u5bf9\u8c61\u4e0a，\u5982\u6c7d\u8f66\u3001\u98de\u673a\u6216\u822a\u5929\u5668\u3002\u76f8\u5bf9\u4e8e\u56fa\u5b9a\u60ef\u6027\u7cfb\u6d4b\u91cf\u7684\u8fd0\u52a8\u5b66\u91cf\u79f0\u4e3a\u7edd\u5bf9\u91cf（\u4f8b\u5982，\u7edd\u5bf9\u52a0\u901f\u5ea6），\u800c\u76f8\u5bf9\u4e8e\u79fb\u52a8\u7cfb\u7edf\u6d4b\u91cf\u7684\u91cf\u79f0\u4e3a\u76f8\u5bf9\u91cf（\u4f8b\u5982，\u76f8\u5bf9\u52a0\u901f\u5ea6）\u3002\u60ef\u6027 XYZ \u7cfb\u7edf\u7684\u5355\u4f4d\u77e2\u91cf\u662f I^\\\\hat{\\\\mathbf{I}}<\/span><\/span><\/span>I<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001J^\\\\hat{\\\\mathbf{J}}<\/span><\/span><\/span>J<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c K^\\\\hat{\\\\mathbf{K}}<\/span><\/span><\/span>K<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u800c\u79fb\u52a8 xyz \u7cfb\u7edf\u7684\u5355\u4f4d\u77e2\u91cf\u662f i^\\\\hat{\\\\mathbf{i}}<\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001j^\\\\hat{\\\\mathbf{j}}<\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c k^\\\\hat{\\\\mathbf{k}}<\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u79fb\u52a8\u7cfb\u7684\u8fd0\u52a8\u662f\u4efb\u610f\u7684，\u5176\u7edd\u5bf9\u89d2\u901f\u5ea6\u4e3a \u03a9\\\\boldsymbol{\\\\Omega}<\/span><\/span>\u03a9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u7136\u800c，\u5982\u679c\u79fb\u52a8\u7cfb\u521a\u6027\u9644\u7740\u5728\u7269\u4f53\u4e0a，\u4f7f\u5176\u4e0d\u4ec5\u968f\u7269\u4f53\u5e73\u79fb\u800c\u4e14\u65cb\u8f6c，\u5219\u8be5\u53c2\u8003\u7cfb\u79f0\u4e3a\u4f53\u5750\u6807\u7cfb，\u8f74\u79f0\u4e3a\u4f53\u8f74\u3002\u4f53\u5750\u6807\u7cfb\u663e\u7136\u4e0e\u5176\u7ed1\u5b9a\u7684\u7269\u4f53\u5177\u6709\u76f8\u540c\u7684\u89d2\u901f\u5ea6\u3002
\n\u8bbe B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4efb\u610f\u65f6\u95f4\u76f8\u5173\u77e2\u91cf\u3002\u5206\u89e3\u4e3a\u6cbf\u60ef\u6027\u53c2\u8003\u7cfb\u7684\u5206\u91cf，\u89e3\u6790\u8868\u793a\u4e3a
\nB=BXI^+BYJ^+BZK^
\n\\\\mathbf {B} = B _ {X} \\\\hat {\\\\mathbf {I}} + B _ {Y} \\\\hat {\\\\mathbf {J}} + B _ {Z} \\\\hat {\\\\mathbf {K}}
\n<\/span><\/span>B<\/span><\/span>=<\/span><\/span><\/span><\/span>B<\/span><\/span>X<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>I<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>Y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>Z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>K<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d BXB_X<\/span><\/span>B<\/span><\/span>X<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001BYB_Y<\/span><\/span>B<\/span><\/span>Y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c BZB_Z<\/span><\/span>B<\/span><\/span>Z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u65f6\u95f4\u7684\u51fd\u6570\u3002\u7531\u4e8e I^\\\\hat{\\\\mathbf{I}}<\/span><\/span><\/span>I<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001J^\\\\hat{\\\\mathbf{J}}<\/span><\/span><\/span>J<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c K^\\\\hat{\\\\mathbf{K}}<\/span><\/span><\/span>K<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u56fa\u5b9a\u7684，B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u65f6\u95f4\u5bfc\u6570\u7b80\u5355\u5730\u7531\u4e0b\u5f0f\u7ed9\u51fa
\ndBdt=dBXdtI^+dBYdtJ^+dBZdtK^
\n\\\\frac {d \\\\mathbf {B}}{d t} = \\\\frac {d B _ {X}}{d t} \\\\hat {\\\\mathbf {I}} + \\\\frac {d B _ {Y}}{d t} \\\\hat {\\\\mathbf {J}} + \\\\frac {d B _ {Z}}{d t} \\\\hat {\\\\mathbf {K}}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>X<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>I<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>Y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>J<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>Z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>K<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\ndBX\/dtdB_X\/dt<\/span><\/span>d<\/span>B<\/span><\/span>X<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span>\u3001dBY\/dtdB_Y\/dt<\/span><\/span>d<\/span>B<\/span><\/span>Y<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span> \u548c dBZ\/dtdB_Z\/dt<\/span><\/span>d<\/span>B<\/span><\/span>Z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span> \u662f B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u7edd\u5bf9\u65f6\u95f4\u5bfc\u6570\u7684\u5206\u91cf\u3002<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

\n \u56fe 1.16<\/b> \u56fa\u5b9a（\u60ef\u6027）\u548c\u79fb\u52a8\u521a\u6027\u53c2\u8003\u7cfb\u3002\n<\/p>\n

B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e5f\u53ef\u4ee5\u5206\u89e3\u4e3a\u6cbf\u79fb\u52a8 xyz \u7cfb\u7684\u5206\u91cf，\u4f7f\u5f97\u5728\u4efb\u4f55\u77ac\u95f4，
\nB=Bxi^+Byj^+Bzk^(1.54)
\n\\\\mathbf {B} = B _ {x} \\\\hat {\\\\mathbf {i}} + B _ {y} \\\\hat {\\\\mathbf {j}} + B _ {z} \\\\hat {\\\\mathbf {k}} \\\\tag {1.54}
\n<\/span><\/span>B<\/span><\/span>=<\/span><\/span><\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.54<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u4f7f\u7528\u6b64\u8868\u8fbe\u5f0f\u8ba1\u7b97 B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u7684\u65f6\u95f4\u5bfc\u6570\u5f97\u51fa
\ndBdt=dBxdti^+dBydtj^+dBzdtk^+Bxdi^dt+Bydj^dt+Bzdk^dt(1.55)
\n\\\\frac {d \\\\mathbf {B}}{d t} = \\\\frac {d B _ {x}}{d t} \\\\hat {\\\\mathbf {i}} + \\\\frac {d B _ {y}}{d t} \\\\hat {\\\\mathbf {j}} + \\\\frac {d B _ {z}}{d t} \\\\hat {\\\\mathbf {k}} + B _ {x} \\\\frac {d \\\\hat {\\\\mathbf {i}}}{d t} + B _ {y} \\\\frac {d \\\\hat {\\\\mathbf {j}}}{d t} + B _ {z} \\\\frac {d \\\\hat {\\\\mathbf {k}}}{d t} \\\\tag {1.55}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.55<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5355\u4f4d\u77e2\u91cf i^\\\\hat{\\\\mathbf{i}}<\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001j^\\\\hat{\\\\mathbf{j}}<\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c k^\\\\hat{\\\\mathbf{k}}<\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u7a7a\u95f4\u4e2d\u4e0d\u662f\u56fa\u5b9a\u7684，\u800c\u662f\u4e0d\u65ad\u6539\u53d8\u65b9\u5411；\u56e0\u6b64，\u5b83\u4eec\u7684\u65f6\u95f4\u5bfc\u6570\u4e0d\u4e3a\u96f6\u3002\u5b83\u4eec\u663e\u7136\u5177\u6709\u6052\u5b9a\u7684\u5927\u5c0f（\u5355\u4f4d），\u5e76\u4e14\u7531\u4e8e\u9644\u7740\u5728 xyz \u7cfb\u4e0a，\u5b83\u4eec\u90fd\u5177\u6709\u89d2\u901f\u5ea6 \u03a9\\\\boldsymbol{\\\\Omega}<\/span><\/span>\u03a9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4ece\u65b9\u7a0b 1.52 \u53ef\u4ee5\u5f97\u51fa
\ndi^dt=\u03a9\u00d7i^dj^dt=\u03a9\u00d7j^dk^dt=\u03a9\u00d7k^
\n\\\\frac {d \\\\hat {\\\\mathbf {i}}}{d t} = \\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {i}} \\\\quad \\\\frac {d \\\\hat {\\\\mathbf {j}}}{d t} = \\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {j}} \\\\quad \\\\frac {d \\\\hat {\\\\mathbf {k}}}{d t} = \\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {k}}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5c06\u8fd9\u4e9b\u4ee3\u5165\u65b9\u7a0b 1.55 \u7684\u53f3\u4fa7\u5f97\u51fa
\ndBdt=dBxdti^+dBydtj^+dBzdtk^+Bx(\u03a9\u00d7i^)+By(\u03a9\u00d7j^)+Bz(\u03a9\u00d7k^)=dBxdti^+dBydtj^+dBzdtk^+(\u03a9\u00d7Bxi^)+(\u03a9\u00d7Byj^)+(\u03a9\u00d7Bzk^)=dBxdti^+dBydtj^+dBzdtk^+\u03a9\u00d7(Bxi^+Byj^+Bzk^)
\n\\\\begin{array}{l} \\\\frac {d \\\\mathbf {B}}{d t} = \\\\frac {d B _ {x}}{d t} \\\\hat {\\\\mathbf {i}} + \\\\frac {d B _ {y}}{d t} \\\\hat {\\\\mathbf {j}} + \\\\frac {d B _ {z}}{d t} \\\\hat {\\\\mathbf {k}} + B _ {x} (\\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {i}}) + B _ {y} (\\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {j}}) + B _ {z} (\\\\boldsymbol {\\\\Omega} \\\\times \\\\hat {\\\\mathbf {k}}) \\\\\\\\ = \\\\frac {d B _ {x}}{d t} \\\\hat {\\\\mathbf {i}} + \\\\frac {d B _ {y}}{d t} \\\\hat {\\\\mathbf {j}} + \\\\frac {d B _ {z}}{d t} \\\\hat {\\\\mathbf {k}} + (\\\\boldsymbol {\\\\Omega} \\\\times B _ {x} \\\\hat {\\\\mathbf {i}}) + (\\\\boldsymbol {\\\\Omega} \\\\times B _ {y} \\\\hat {\\\\mathbf {j}}) + (\\\\boldsymbol {\\\\Omega} \\\\times B _ {z} \\\\hat {\\\\mathbf {k}}) \\\\\\\\ = \\\\frac {d B _ {x}}{d t} \\\\hat {\\\\mathbf {i}} + \\\\frac {d B _ {y}}{d t} \\\\hat {\\\\mathbf {j}} + \\\\frac {d B _ {z}}{d t} \\\\hat {\\\\mathbf {k}} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\left(B _ {x} \\\\hat {\\\\mathbf {i}} + B _ {y} \\\\hat {\\\\mathbf {j}} + B _ {z} \\\\hat {\\\\mathbf {k}}\\\\right) \\\\\\\\ \\\\end{array}
\n<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>(<\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u9274\u4e8e\u65b9\u7a0b 1.54，\u8fd9\u53ef\u4ee5\u5199\u6210
\ndBdt=dBdt)rel+\u03a9\u00d7B(1.56)
\n\\\\left. \\\\frac {d \\\\mathbf {B}}{d t} = \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\mathbf {B} \\\\tag {1.56}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span>(<\/span>1.56<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d
\ndBdt)rel=dBxdti^+dBydtj^+dBzdtk^(1.57)
\n\\\\left. \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} = \\\\frac {d B _ {x}}{d t} \\\\hat {\\\\mathbf {i}} + \\\\frac {d B _ {y}}{d t} \\\\hat {\\\\mathbf {j}} + \\\\frac {d B _ {z}}{d t} \\\\hat {\\\\mathbf {k}} \\\\tag {1.57}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.57<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\ndB\/dt)reld\\\\mathbf{B}\/dt)_{\\\\text{rel}}<\/span><\/span>d<\/span>B<\/span>\/<\/span>d<\/span>t<\/span>)<\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f B\\\\mathbf{B}<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u76f8\u5bf9\u4e8e\u79fb\u52a8\u7cfb\u7684\u65f6\u95f4\u5bfc\u6570\u3002\u65b9\u7a0b 1.56 \u663e\u793a\u4e86\u5982\u4f55\u4ece\u76f8\u5bf9\u65f6\u95f4\u5bfc\u6570\u83b7\u5f97\u7edd\u5bf9\u65f6\u95f4\u5bfc\u6570\u3002\u663e\u7136，\u4ec5\u5f53\u79fb\u52a8\u7cfb\u5904\u4e8e\u7eaf\u5e73\u79fb (\u03a9=0)(\\\\boldsymbol{\\\\Omega} = \\\\mathbf{0})<\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span> \u65f6，dB\/dt=dB\/dt)reld\\\\mathbf{B}\/dt = d\\\\mathbf{B}\/dt)_{\\\\text{rel}}<\/span><\/span>d<\/span>B<\/span>\/<\/span>d<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>B<\/span>\/<\/span>d<\/span>t<\/span>)<\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002
\n\u65b9\u7a0b 1.56 \u53ef\u4ee5\u9012\u5f52\u5730\u7528\u4e8e\u8ba1\u7b97\u9ad8\u9636\u65f6\u95f4\u5bfc\u6570\u3002\u56e0\u6b64，\u5bf9\u65b9\u7a0b 1.56 \u5bf9 tt<\/span><\/span>t<\/span><\/span><\/span><\/span><\/span> \u6c42\u5bfc，\u6211\u4eec\u5f97\u5230
\nd2Bdt2=ddtdBdt)rel+d\u03a9dt\u00d7B+\u03a9\u00d7dBdt
\n\\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}} = \\\\left. \\\\frac {d}{d t} \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} + \\\\frac {d \\\\boldsymbol {\\\\Omega}}{d t} \\\\times \\\\mathbf {B} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\frac {d \\\\mathbf {B}}{d t}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03a9<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5728\u6700\u540e\u4e00\u9879\u4e2d\u4f7f\u7528\u65b9\u7a0b 1.56 \u5f97\u51fa
\nd2Bdt2=ddtdBdt)rel+d\u03a9dt\u00d7B+\u03a9\u00d7[dBdt)rel+\u03a9\u00d7B(1.58)
\n\\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}} = \\\\left. \\\\frac {d}{d t} \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} + \\\\frac {d \\\\boldsymbol {\\\\Omega}}{d t} \\\\times \\\\mathbf {B} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\left[ \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\mathbf {B} \\\\tag {1.58}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03a9<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span>(<\/span>1.58<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u65b9\u7a0b 1.56 \u4e5f\u610f\u5473\u7740
\nddtdBdt)rel=d2Bdt2)rel+\u03a9\u00d7dBdt)rel(1.59)
\n\\\\left. \\\\frac {d}{d t} \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} = \\\\left. \\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}}\\\\right) _ {\\\\text {rel}} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\left. \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} \\\\tag {1.59}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.59<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d
\nd2Bdt2)rel=d2Bxdt2i^+d2Bydt2j^+d2Bzdt2k^
\n\\\\left. \\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}}\\\\right) _ {\\\\mathrm {rel}} = \\\\frac {d ^ {2} B _ {x}}{d t ^ {2}} \\\\hat {\\\\mathbf {i}} + \\\\frac {d ^ {2} B _ {y}}{d t ^ {2}} \\\\hat {\\\\mathbf {j}} + \\\\frac {d ^ {2} B _ {z}}{d t ^ {2}} \\\\hat {\\\\mathbf {k}}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5c06\u65b9\u7a0b 1.59 \u4ee3\u5165\u65b9\u7a0b 1.58 \u5f97\u51fa
\nd2Bdt2=[d2Bdt2]rel+\u03a9\u00d7dBdt)rel+d\u03a9dt\u00d7B+\u03a9\u00d7[dBdt)rel+\u03a9\u00d7B
\n\\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}} = \\\\left[ \\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}} \\\\right] _ {\\\\mathrm {rel}} + \\\\left. \\\\boldsymbol {\\\\Omega} \\\\times \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\mathrm {rel}} + \\\\frac {d \\\\boldsymbol {\\\\Omega}}{d t} \\\\times \\\\mathbf {B} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\left[ \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\mathrm {rel}} + \\\\boldsymbol {\\\\Omega} \\\\times \\\\mathbf {B}
\n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03a9<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5408\u5e76\u9879，\u8fd9\u53d8\u4e3a
\nd2Bdt2=d2Bdt2)rel+\u03a9\u02d9\u00d7B+\u03a9\u00d7(\u03a9\u00d7B)+2\u03a9\u00d7dBdt)rel(1.60)
\n\\\\left. \\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}} = \\\\frac {d ^ {2} \\\\mathbf {B}}{d t ^ {2}}\\\\right) _ {\\\\text {rel}} + \\\\dot {\\\\boldsymbol {\\\\Omega}} \\\\times \\\\mathbf {B} + \\\\boldsymbol {\\\\Omega} \\\\times (\\\\boldsymbol {\\\\Omega} \\\\times \\\\mathbf {B}) + 2 \\\\boldsymbol {\\\\Omega} \\\\times \\\\left. \\\\frac {d \\\\mathbf {B}}{d t}\\\\right) _ {\\\\text {rel}} \\\\tag {1.60}
\n<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>(<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>B<\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>\u03a9<\/span><\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>B<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>rel<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>1.60<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\n\u5176\u4e2d \u03a9\u02d9\u2261d\u03a9\/dt\\\\dot{\\\\boldsymbol{\\\\Omega}} \\\\equiv d\\\\boldsymbol{\\\\Omega}\/dt<\/span><\/span><\/span>\u03a9<\/span><\/span><\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2261<\/span><\/span><\/span><\/span>d<\/span>\u03a9<\/span><\/span><\/span>\/<\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span> \u662f xyz \u7cfb\u7684\u7edd\u5bf9\u89d2\u52a0\u901f\u5ea6\u3002
\n\u9ad8\u9636\u65f6\u95f4\u5bfc\u6570\u7684\u516c\u5f0f\u4ee5\u7c7b\u4f3c\u7684\u65b9\u5f0f\u627e\u5230\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u7b2c1\u7ae0-\u8d28\u70b9\u52a8\u529b\u5b66（\u4e2d）
\n1.5 \u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b
\n\u529b\u4e0d\u50cf\u8d28\u91cf\u90a3\u6837\u662f\u4e00\u4e2a\u539f\u59cb\u6982\u5ff5，\u56e0\u4e3a\u5b83\u4e0e\u8fd0\u52a8\u548c\u60ef\u6027\u7684\u6982\u5ff5\u5bc6\u5207\u76f8\u5173\u3002\u4e8b\u5b9e\u4e0a，\u6539\u53d8\u7269\u4f53\u8fd0\u52a8\u7684\u552f\u4e00\u65b9\u6cd5\u662f\u5bf9\u5176\u65bd\u52a0\u529b\u3002\u8fd0\u52a8\u6539\u53d8\u7684\u7a0b\u5ea6\u662f\u529b\u7684\u91cf\u5ea6\u3002\u725b\u987f\u7b2c\u4e8c\u8fd0\u52a8\u5b9a\u5f8b\u91cf\u5316\u4e86\u8fd9\u4e00\u70b9\u3002\u5982\u679c\u8d28\u91cf\u4e3a mmm \u7684\u7269\u4f53\u4e0a\u7684\u5408\u529b\u6216\u51c0\u529b\u662f Fnet\\\\mathbf{F}_{\\\\text{net}}Fnet\u200b，\u5219
\nFnetma(1.38)
\n\\\\mathbf {F} _ {\\\\text {net}} <\/p>\n","protected":false},"author":2,"featured_media":79769,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[6534],"topic":[],"class_list":["post-79774","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-6534"],"yoast_head":"\n\u3010\u7ffb\u8bd1\u3011\u9762\u5411\u5de5\u79d1\u5b66\u751f\u7684\u8f68\u9053\u529b\u5b66-\u7b2c1\u7ae0-\u8d28\u70b9\u52a8\u529b\u5b66\uff08Part 2\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/79774.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010\u7ffb\u8bd1\u3011\u9762\u5411\u5de5\u79d1\u5b66\u751f\u7684\u8f68\u9053\u529b\u5b66-\u7b2c1\u7ae0-\u8d28\u70b9\u52a8\u529b\u5b66\uff08Part 2\uff09 - 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