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z}dz",[61,936,938,962,1054,1148],{"className":937,"ariaHidden":110},[109],[61,939,941,944,947,953,956,959],{"className":940},[114],[61,942],{"className":943,"style":407},[118],[61,945,87],{"className":946},[123,167],[61,948,950],{"className":949,"style":200},[123],[61,951,52],{"className":952,"style":204},[123,167],[61,954],{"className":955,"style":544},[543],[61,957,444],{"className":958},[548],[61,960],{"className":961,"style":544},[543],[61,963,965,968,1039,1042,1045,1048,1051],{"className":964},[114],[61,966],{"className":967,"style":558},[118],[61,969,971,974,1036],{"className":970},[123],[61,972],{"className":973},[127,128],[61,975,977],{"className":976},[80],[61,978,980,1028],{"className":979},[135,136],[61,981,983,1025],{"className":982},[140],[61,984,986,1000,1008],{"className":985,"style":577},[144],[61,987,988,991],{"style":580},[61,989],{"className":990,"style":153},[152],[61,992,994,997],{"className":993},[123],[61,995,455],{"className":996,"style":590},[123],[61,998,877],{"className":999},[123,167],[61,1001,1002,1005],{"style":173},[61,1003],{"className":1004,"style":153},[152],[61,1006],{"className":1007,"style":181},[180],[61,1009,1010,1013],{"style":604},[61,1011],{"className":1012,"style":153},[152],[61,1014,1016,1019],{"className":1015},[123],[61,1017,455],{"className":1018,"style":590},[123],[61,1020,1022],{"className":1021,"style":200},[123],[61,1023,52],{"className":1024,"style":204},[123,167],[61,1026,209],{"className":1027},[208],[61,1029,1031],{"className":1030},[140],[61,1032,1034],{"className":1033,"style":629},[144],[61,1035],{},[61,1037],{"className":1038},[222,128],[61,1040,87],{"className":1041},[123,167],[61,1043,877],{"className":1044},[123,167],[61,1046],{"className":1047,"style":644},[543],[61,1049,472],{"className":1050},[648],[61,1052],{"className":1053,"style":644},[543],[61,1055,1057,1061,1133,1136,1139,1142,1145],{"className":1056},[114],[61,1058],{"className":1059,"style":1060},[118],"height:2.2519em;vertical-align:-0.8804em;",[61,1062,1064,1067,1130],{"className":1063},[123],[61,1065],{"className":1066},[127,128],[61,1068,1070],{"className":1069},[80],[61,1071,1073,1121],{"className":1072},[135,136],[61,1074,1076,1118],{"className":1075},[140],[61,1077,1079,1093,1101],{"className":1078,"style":577},[144],[61,1080,1081,1084],{"style":580},[61,1082],{"className":1083,"style":153},[152],[61,1085,1087,1090],{"className":1086},[123],[61,1088,455],{"className":1089,"style":590},[123],[61,1091,902],{"className":1092,"style":333},[123,167],[61,1094,1095,1098],{"style":173},[61,1096],{"className":1097,"style":153},[152],[61,1099],{"className":1100,"style":181},[180],[61,1102,1103,1106],{"style":604},[61,1104],{"className":1105,"style":153},[152],[61,1107,1109,1112],{"className":1108},[123],[61,1110,455],{"className":1111,"style":590},[123],[61,1113,1115],{"className":1114,"style":200},[123],[61,1116,52],{"className":1117,"style":204},[123,167],[61,1119,209],{"className":1120},[208],[61,1122,1124],{"className":1123},[140],[61,1125,1128],{"className":1126,"style":1127},[144],"height:0.8804em;",[61,1129],{},[61,1131],{"className":1132},[222,128],[61,1134,87],{"className":1135},[123,167],[61,1137,902],{"className":1138,"style":333},[123,167],[61,1140],{"className":1141,"style":644},[543],[61,1143,472],{"className":1144},[648],[61,1146],{"className":1147,"style":644},[543],[61,1149,1151,1154,1226,1229],{"className":1150},[114],[61,1152],{"className":1153,"style":558},[118],[61,1155,1157,1160,1223],{"className":1156},[123],[61,1158],{"className":1159},[127,128],[61,1161,1163],{"className":1162},[80],[61,1164,1166,1215],{"className":1165},[135,136],[61,1167,1169,1212],{"className":1168},[140],[61,1170,1172,1187,1195],{"className":1171,"style":577},[144],[61,1173,1174,1177],{"style":580},[61,1175],{"className":1176,"style":153},[152],[61,1178,1180,1183],{"className":1179},[123],[61,1181,455],{"className":1182,"style":590},[123],[61,1184,927],{"className":1185,"style":1186},[123,167],"margin-right:0.044em;",[61,1188,1189,1192],{"style":173},[61,1190],{"className":1191,"style":153},[152],[61,1193],{"className":1194,"style":181},[180],[61,1196,1197,1200],{"style":604},[61,1198],{"className":1199,"style":153},[152],[61,1201,1203,1206],{"className":1202},[123],[61,1204,455],{"className":1205,"style":590},[123],[61,1207,1209],{"className":1208,"style":200},[123],[61,1210,52],{"className":1211,"style":204},[123,167],[61,1213,209],{"className":1214},[208],[61,1216,1218],{"className":1217},[140],[61,1219,1221],{"className":1220,"style":629},[144],[61,1222],{},[61,1224],{"className":1225},[222,128],[61,1227,87],{"className":1228},[123,167],[61,1230,927],{"className":1231,"style":1186},[123,167],[14,1233,1234],{},"其中由几何运算：",[14,1236,1237,1350,1351],{},[61,1238,1240,1270],{"className":1239},[64],[61,1241,1243],{"className":1242},[68],[70,1244,1245],{"xmlns":72},[74,1246,1247,1267],{},[77,1248,1249],{},[89,1250,1251],{"scriptlevel":447,"displaystyle":110},[80,1252,1253,1261],{},[77,1254,1255,1257],{},[85,1256,455],{"mathvariant":454},[89,1258,1259],{"style":91},[85,1260,52],{},[77,1262,1263,1265],{},[85,1264,455],{"mathvariant":454},[85,1266,877],{},[102,1268,1269],{"encoding":104},"\\dfrac{\\partial \\pmb{r}}{\\partial x}",[61,1271,1273],{"className":1272,"ariaHidden":110},[109],[61,1274,1276,1279],{"className":1275},[114],[61,1277],{"className":1278,"style":558},[118],[61,1280,1282,1285,1347],{"className":1281},[123],[61,1283],{"className":1284},[127,128],[61,1286,1288],{"className":1287},[80],[61,1289,1291,1339],{"className":1290},[135,136],[61,1292,1294,1336],{"className":1293},[140],[61,1295,1297,1311,1319],{"className":1296,"style":577},[144],[61,1298,1299,1302],{"style":580},[61,1300],{"className":1301,"style":153},[152],[61,1303,1305,1308],{"className":1304},[123],[61,1306,455],{"className":1307,"style":590},[123],[61,1309,877],{"className":1310},[123,167],[61,1312,1313,1316],{"style":173},[61,1314],{"className":1315,"style":153},[152],[61,1317],{"className":1318,"style":181},[180],[61,1320,1321,1324],{"style":604},[61,1322],{"className":1323,"style":153},[152],[61,1325,1327,1330],{"className":1326},[123],[61,1328,455],{"className":1329,"style":590},[123],[61,1331,1333],{"className":1332,"style":200},[123],[61,1334,52],{"className":1335,"style":204},[123,167],[61,1337,209],{"className":1338},[208],[61,1340,1342],{"className":1341},[140],[61,1343,1345],{"className":1344,"style":629},[144],[61,1346],{},[61,1348],{"className":1349},[222,128],"即为沿x轴方向单位矢量",[61,1352,1354,1376],{"className":1353},[64],[61,1355,1357],{"className":1356},[68],[70,1358,1359],{"xmlns":72},[74,1360,1361,1373],{},[77,1362,1363],{},[89,1364,1365],{"style":91},[1366,1367,1368,1370],"mover",{"accent":110},[85,1369,877],{},[442,1371,1372],{},"^",[102,1374,1375],{"encoding":104},"\\pmb{\\hat{x}}",[61,1377,1379],{"className":1378,"ariaHidden":110},[109],[61,1380,1382,1385],{"className":1381},[114],[61,1383],{"className":1384,"style":407},[118],[61,1386,1388],{"className":1387,"style":200},[123],[61,1389,1392],{"className":1390},[123,1391],"accent",[61,1393,1395],{"className":1394},[135],[61,1396,1398],{"className":1397},[140],[61,1399,1401,1410],{"className":1400,"style":407},[144],[61,1402,1404,1407],{"style":1403},"top:-3em;",[61,1405],{"className":1406,"style":153},[152],[61,1408,877],{"className":1409},[123,167],[61,1411,1412,1415],{"style":1403},[61,1413],{"className":1414,"style":153},[152],[61,1416,1420],{"className":1417,"style":1419},[1418],"accent-body","left:-0.2222em;",[61,1421,1372],{"className":1422},[123],[14,1424,1425,1538,1539,209],{},[61,1426,1428,1458],{"className":1427},[64],[61,1429,1431],{"className":1430},[68],[70,1432,1433],{"xmlns":72},[74,1434,1435,1455],{},[77,1436,1437],{},[89,1438,1439],{"scriptlevel":447,"displaystyle":110},[80,1440,1441,1449],{},[77,1442,1443,1445],{},[85,1444,455],{"mathvariant":454},[89,1446,1447],{"style":91},[85,1448,52],{},[77,1450,1451,1453],{},[85,1452,455],{"mathvariant":454},[85,1454,902],{},[102,1456,1457],{"encoding":104},"\\dfrac{\\partial \\pmb{r}}{\\partial y}",[61,1459,1461],{"className":1460,"ariaHidden":110},[109],[61,1462,1464,1467],{"className":1463},[114],[61,1465],{"className":1466,"style":1060},[118],[61,1468,1470,1473,1535],{"className":1469},[123],[61,1471],{"className":1472},[127,128],[61,1474,1476],{"className":1475},[80],[61,1477,1479,1527],{"className":1478},[135,136],[61,1480,1482,1524],{"className":1481},[140],[61,1483,1485,1499,1507],{"className":1484,"style":577},[144],[61,1486,1487,1490],{"style":580},[61,1488],{"className":1489,"style":153},[152],[61,1491,1493,1496],{"className":1492},[123],[61,1494,455],{"className":1495,"style":590},[123],[61,1497,902],{"className":1498,"style":333},[123,167],[61,1500,1501,1504],{"style":173},[61,1502],{"className":1503,"style":153},[152],[61,1505],{"className":1506,"style":181},[180],[61,1508,1509,1512],{"style":604},[61,1510],{"className":1511,"style":153},[152],[61,1513,1515,1518],{"className":1514},[123],[61,1516,455],{"className":1517,"style":590},[123],[61,1519,1521],{"className":1520,"style":200},[123],[61,1522,52],{"className":1523,"style":204},[123,167],[61,1525,209],{"className":1526},[208],[61,1528,1530],{"className":1529},[140],[61,1531,1533],{"className":1532,"style":1127},[144],[61,1534],{},[61,1536],{"className":1537},[222,128],"即为沿y轴方向单位矢量",[61,1540,1542,1562],{"className":1541},[64],[61,1543,1545],{"className":1544},[68],[70,1546,1547],{"xmlns":72},[74,1548,1549,1559],{},[77,1550,1551],{},[89,1552,1553],{"style":91},[1366,1554,1555,1557],{"accent":110},[85,1556,902],{},[442,1558,1372],{},[102,1560,1561],{"encoding":104},"\\pmb{\\hat{y}}",[61,1563,1565],{"className":1564,"ariaHidden":110},[109],[61,1566,1568,1572],{"className":1567},[114],[61,1569],{"className":1570,"style":1571},[118],"height:0.8889em;vertical-align:-0.1944em;",[61,1573,1575],{"className":1574,"style":200},[123],[61,1576,1578],{"className":1577},[123,1391],[61,1579,1581,1610],{"className":1580},[135,136],[61,1582,1584,1607],{"className":1583},[140],[61,1585,1587,1595],{"className":1586,"style":407},[144],[61,1588,1589,1592],{"style":1403},[61,1590],{"className":1591,"style":153},[152],[61,1593,902],{"className":1594,"style":333},[123,167],[61,1596,1597,1600],{"style":1403},[61,1598],{"className":1599,"style":153},[152],[61,1601,1604],{"className":1602,"style":1603},[1418],"left:-0.1944em;",[61,1605,1372],{"className":1606},[123],[61,1608,209],{"className":1609},[208],[61,1611,1613],{"className":1612},[140],[61,1614,1617],{"className":1615,"style":1616},[144],"height:0.1944em;",[61,1618],{},[14,1620,1621,1734,1735,209],{},[61,1622,1624,1654],{"className":1623},[64],[61,1625,1627],{"className":1626},[68],[70,1628,1629],{"xmlns":72},[74,1630,1631,1651],{},[77,1632,1633],{},[89,1634,1635],{"scriptlevel":447,"displaystyle":110},[80,1636,1637,1645],{},[77,1638,1639,1641],{},[85,1640,455],{"mathvariant":454},[89,1642,1643],{"style":91},[85,1644,52],{},[77,1646,1647,1649],{},[85,1648,455],{"mathvariant":454},[85,1650,927],{},[102,1652,1653],{"encoding":104},"\\dfrac{\\partial 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23,167,160],[61,6547,6549],{"className":6548,"style":200},[123,160],[61,6550,6552],{"className":6551},[123,1391,160],[61,6553,6555],{"className":6554},[135],[61,6556,6558],{"className":6557},[140],[61,6559,6561,6569],{"className":6560,"style":4238},[144],[61,6562,6563,6566],{"style":6441},[61,6564],{"className":6565,"style":6445},[152],[61,6567,3519],{"className":6568,"style":204},[123,167,160],[61,6570,6572,6575],{"style":6571},"top:-2.9634em;",[61,6573],{"className":6574,"style":6445},[152],[61,6576,6578],{"className":6577,"style":5095},[1418],[61,6579,1372],{"className":6580},[123,160],[61,6582,209],{"className":6583},[208],[61,6585,6587],{"className":6586},[140],[61,6588,6590],{"className":6589,"style":216},[144],[61,6591],{},[61,6593],{"className":6594},[222,128],"怎么处理",[61,6597,6599,6614],{"className":6598},[64],[61,6600,6602],{"className":6601},[68],[70,6603,6604],{"xmlns":72},[74,6605,6606,6611],{},[77,6607,6608],{},[442,6609,6610],{},"⟶",[102,6612,6613],{"encoding":104},"\\longrightarrow",[61,6615,6617],{"className":6616,"ariaHidden":110},[109],[61,6618,6620,6624],{"className":6619},[114],[61,6621],{"className":6622,"style":6623},[118],"height:0.522em;vertical-align:-0.011em;",[61,6625,6610],{"className":6626},[548],"利用全微分处理，",[61,6629,6631,6665],{"className":6630},[64],[61,6632,6634],{"className":6633},[68],[70,6635,6636],{"xmlns":72},[74,6637,6638,6662],{},[77,6639,6640,6642,6650,6652,6654],{},[85,6641,87],{},[89,6643,6644],{"style":91},[1366,6645,6646,6648],{"accent":110},[85,6647,3494],{},[442,6649,1372],{},[1817,6651,6331],{},[85,6653,87],{},[89,6655,6656],{"style":91},[1366,6657,6658,6660],{"accent":110},[85,6659,3519],{},[442,6661,1372],{},[102,6663,6664],{"encoding":104},"d\\pmb{\\hat{\\rho}}和d\\pmb{\\hat{\\theta}}",[61,6666,6668],{"className":6667,"ariaHidden":110},[109],[61,6669,6671,6674,6677,6722,6725,6728],{"className":6670},[114],[61,6672],{"className":6673,"style":4222},[118],[61,6675,87],{"className":6676},[123,167],[61,6678,6680],{"className":6679,"style":200},[123],[61,6681,6683],{"className":6682},[123,1391],[61,6684,6686,6714],{"className":6685},[135,136],[61,6687,6689,6711],{"className":6688},[140],[61,6690,6692,6700],{"className":6691,"style":407},[144],[61,6693,6694,6697],{"style":1403},[61,6695],{"className":6696,"style":153},[152],[61,6698,3494],{"className":6699},[123,167],[61,6701,6702,6705],{"style":1403},[61,6703],{"className":6704,"style":153},[152],[61,6706,6708],{"className":6707,"style":5095},[1418],[61,6709,1372],{"className":6710},[123],[61,6712,209],{"className":6713},[208],[61,6715,6717],{"className":6716},[140],[61,6718,6720],{"className":6719,"style":1616},[144],[61,6721],{},[61,6723,6331],{"className":6724},[123,1885],[61,6726,87],{"className":6727},[123,167],[61,6729,6731],{"className":6730,"style":200},[123],[61,6732,6734],{"className":6733},[123,1391],[61,6735,6737],{"className":6736},[135],[61,6738,6740],{"className":6739},[140],[61,6741,6743,6751],{"className":6742,"style":4238},[144],[61,6744,6745,6748],{"style":1403},[61,6746],{"className":6747,"style":153},[152],[61,6749,3519],{"className":6750,"style":204},[123,167],[61,6752,6753,6756],{"style":4252},[61,6754],{"className":6755,"style":153},[152],[61,6757,6759],{"className":6758,"style":5095},[1418],[61,6760,1372],{"className":6761},[123],"对坐标的全微分是可以获得的：",[61,6764,6766],{"className":6765},[421],[61,6767,6769,6978],{"className":6768},[64],[61,6770,6772],{"className":6771},[68],[70,6773,6774],{"xmlns":72,"display":430},[74,6775,6776,6975],{},[77,6777,6778,6780,6788,6790,6810,6812,6814,6816,6836,6838,6840,6843,6845,6848,6850,6852,6854,6857,6865,6867,6869,6877,6879,6899,6901,6903,6905,6925,6927,6929,6931,6933,6935,6937,6939,6943,6946,6954,6957,6959,6961,6963,6965,6967],{},[85,6779,87],{},[89,6781,6782],{"style":91},[1366,6783,6784,6786],{"accent":110},[85,6785,3494],{},[442,6787,1372],{},[442,6789,444],{},[80,6791,6792,6804],{},[77,6793,6794,6796],{},[85,6795,455],{"mathvariant":454},[89,6797,6798],{"style":91},[1366,6799,6800,6802],{"accent":110},[85,6801,3494],{},[442,6803,1372],{},[77,6805,6806,6808],{},[85,6807,455],{"mathvariant":454},[85,6809,3494],{},[85,6811,87],{},[85,6813,3494],{},[442,6815,472],{},[80,6817,6818,6830],{},[77,6819,6820,6822],{},[85,6821,455],{"mathvariant":454},[89,6823,6824],{"style":91},[1366,6825,6826,6828],{"accent":110},[85,6827,3494],{},[442,6829,1372],{},[77,6831,6832,6834],{},[85,6833,455],{"mathvariant":454},[85,6835,3519],{},[85,6837,87],{},[85,6839,3519],{},[543,6841],{"linebreak":6842},"newline",[442,6844,444],{},[6846,6847,447],"mn",{},[442,6849,472],{},[85,6851,87],{},[85,6853,3519],{},[442,6855,6856],{},"⋅",[89,6858,6859],{"style":91},[1366,6860,6861,6863],{"accent":110},[85,6862,3519],{},[442,6864,1372],{},[543,6866],{"linebreak":6842},[85,6868,87],{},[89,6870,6871],{"style":91},[1366,6872,6873,6875],{"accent":110},[85,6874,3519],{},[442,6876,1372],{},[442,6878,444],{},[80,6880,6881,6893],{},[77,6882,6883,6885],{},[85,6884,455],{"mathvariant":454},[89,6886,6887],{"style":91},[1366,6888,6889,6891],{"accent":110},[85,6890,3519],{},[442,6892,1372],{},[77,6894,6895,6897],{},[85,6896,455],{"mathvariant":454},[85,6898,3494],{},[85,6900,87],{},[85,6902,3494],{},[442,6904,472],{},[80,6906,6907,6919],{},[77,6908,6909,6911],{},[85,6910,455],{"mathvariant":454},[89,6912,6913],{"style":91},[1366,6914,6915,6917],{"accent":110},[85,6916,3519],{},[442,6918,1372],{},[77,6920,6921,6923],{},[85,6922,455],{"mathvariant":454},[85,6924,3519],{},[85,6926,87],{},[85,6928,3519],{},[543,6930],{"linebreak":6842},[442,6932,444],{},[85,6934,87],{},[85,6936,3494],{},[442,6938,6856],{},[442,6940,6942],{"stretchy":6941},"false","(",[442,6944,6945],{},"−",[89,6947,6948],{"style":91},[1366,6949,6950,6952],{"accent":110},[85,6951,3494],{},[442,6953,1372],{},[442,6955,6956],{"stretchy":6941},")",[442,6958,444],{},[442,6960,6945],{},[85,6962,87],{},[85,6964,3494],{},[442,6966,6856],{},[89,6968,6969],{"style":91},[1366,6970,6971,6973],{"accent":110},[85,6972,3494],{},[442,6974,1372],{},[102,6976,6977],{"encoding":104},"d\\pmb{\\hat{\\rho}}=\\frac{\\partial\\pmb{\\hat{\\rho}}}{\\partial\\rho}d\\rho+\\frac{\\partial\\pmb{\\hat{\\rho}}}{\\partial\\theta}d\\theta\n\\\\\n=0+d\\theta\\cdot\\pmb{\\hat{\\theta}}\n\\\\\nd\\pmb{\\hat{\\theta}}=\\frac{\\partial\\pmb{\\hat{\\theta}}}{\\partial\\rho}d\\rho+\\frac{\\partial\\pmb{\\hat{\\theta}}}{\\partial\\theta}d\\theta\n\\\\\n=d\\rho\\cdot(-\\pmb{\\hat{\\rho}})=-d\\rho\\cdot\\pmb{\\hat{\\rho}}",[61,6979,6981,7044,7175,7297,7300,7312,7331,7352,7392,7395,7447,7568,7679,7682,7694,7715,7785,7809],{"className":6980,"ariaHidden":110},[109],[61,6982,6984,6987,6990,7035,7038,7041],{"className":6983},[114],[61,6985],{"className":6986,"style":1571},[118],[61,6988,87],{"className":6989},[123,167],[61,6991,6993],{"className":6992,"style":200},[123],[61,6994,6996],{"className":6995},[123,1391],[61,6997,6999,7027],{"className":6998},[135,136],[61,7000,7002,7024],{"className":7001},[140],[61,7003,7005,7013],{"className":7004,"style":407},[144],[61,7006,7007,7010],{"style":1403},[61,7008],{"className":7009,"style":153},[152],[61,7011,3494],{"className":7012},[123,167],[61,7014,7015,7018],{"style":1403},[61,7016],{"className":7017,"style":153},[152],[61,7019,7021],{"className":7020,"style":5095},[1418],[61,7022,1372],{"className":7023},[123],[61,7025,209],{"className":7026},[208],[61,7028,7030],{"className":7029},[140],[61,7031,7033],{"className":7032,"style":1616},[144],[61,7034],{},[61,7036],{"className":7037,"style":544},[543],[61,7039,444],{"className":7040},[548],[61,7042],{"className":7043,"style":544},[543],[61,7045,7047,7050,7160,7163,7166,7169,7172],{"className":7046},[114],[61,7048],{"className":7049,"style":1060},[118],[61,7051,7053,7056,7157],{"className":7052},[123],[61,7054],{"className":7055},[127,128],[61,7057,7059],{"className":7058},[80],[61,7060,7062,7149],{"className":7061},[135,136],[61,7063,7065,7146],{"className":7064},[140],[61,7066,7068,7082,7090],{"className":7067,"style":577},[144],[61,7069,7070,7073],{"style":580},[61,7071],{"className":7072,"style":153},[152],[61,7074,7076,7079],{"className":7075},[123],[61,7077,455],{"className":7078,"style":590},[123],[61,7080,3494],{"className":7081},[123,167],[61,7083,7084,7087],{"style":173},[61,7085],{"className":7086,"style":153},[152],[61,7088],{"className":7089,"style":181},[180],[61,7091,7092,7095],{"style":604},[61,7093],{"className":7094,"style":153},[152],[61,7096,7098,7101],{"className":7097},[123],[61,7099,455],{"className":7100,"style":590},[123],[61,7102,7104],{"className":7103,"style":200},[123],[61,7105,7107],{"className":7106},[123,1391],[61,7108,7110,7138],{"className":7109},[135,136],[61,7111,7113,7135],{"className":7112},[140],[61,7114,7116,7124],{"className":7115,"style":407},[144],[61,7117,7118,7121],{"style":1403},[61,7119],{"className":7120,"style":153},[152],[61,7122,3494],{"className":7123},[123,167],[61,7125,7126,7129],{"style":1403},[61,7127],{"className":7128,"style":153},[152],[61,7130,7132],{"className":7131,"style":5095},[1418],[61,7133,1372],{"className":7134},[123],[61,7136,209],{"className":7137},[208],[61,7139,7141],{"className":7140},[140],[61,7142,7144],{"className":7143,"style":1616},[144],[61,7145],{},[61,7147,209],{"className":7148},[208],[61,7150,7152],{"className":7151},[140],[61,7153,7155],{"className":7154,"style":1127},[144],[61,7156],{},[61,7158],{"className":7159},[222,128],[61,7161,87],{"className":7162},[123,167],[61,7164,3494],{"className":7165},[123,167],[61,7167],{"className":7168,"style":644},[543],[61,7170,472],{"className":7171},[648],[61,7173],{"className":7174,"style":644},[543],[61,7176,7178,7181,7291,7294],{"className":7177},[114],[61,7179],{"className":7180,"style":558},[118],[61,7182,7184,7187,7288],{"className":7183},[123],[61,7185],{"className":7186},[127,128],[61,7188,7190],{"className":7189},[80],[61,7191,7193,7280],{"className":7192},[135,136],[61,7194,7196,7277],{"className":7195},[140],[61,7197,7199,7213,7221],{"className":7198,"style":577},[144],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1,9785,9787,9800],{"className":9786},[64],[61,9788,9790],{"className":9789},[68],[70,9791,9792],{"xmlns":72},[74,9793,9794,9798],{},[77,9795,9796],{},[442,9797,6610],{},[102,9799,6613],{"encoding":104},[61,9801,9803],{"className":9802,"ariaHidden":110},[109],[61,9804,9806,9809],{"className":9805},[114],[61,9807],{"className":9808,"style":6623},[118],[61,9810,6610],{"className":9811},[548],"把运动分解为直线运动和圆周运动",[24,9814,9815,9828,9840,9954],{},[14,9816,9817],{},[9818,9819,9820,9821,9827],"mark",{},"其",[9822,9823,9824],"em",{},[50,9825,9826],{},"本质","是对于速度矢量的大小和方向进行度量",[14,9829,9830],{},[228,9831,9835],{"href":9832,"rel":9833},"https:\u002F\u002Fimgse.com\u002Fi\u002FpFMYz0f",[9834],"nofollow",[9836,9837],"img",{"alt":9838,"src":9839},"curve.jpg","https:\u002F\u002Fs11.ax1x.com\u002F2024\u002F02\u002F01\u002FpFMYz0f.jpg",[14,9841,9842,9843,9871,9872,9909,9912,9945,9946,9953],{},"这里其实用到了一个思想",[61,9844,9846,9859],{"className":9845},[64],[61,9847,9849],{"className":9848},[68],[70,9850,9851],{"xmlns":72},[74,9852,9853,9857],{},[77,9854,9855],{},[442,9856,6610],{},[102,9858,6613],{"encoding":104},[61,9860,9862],{"className":9861,"ariaHidden":110},[109],[61,9863,9865,9868],{"className":9864},[114],[61,9866],{"className":9867,"style":6623},[118],[61,9869,6610],{"className":9870},[548],"将时间项",[61,9873,9875,9892],{"className":9874},[64],[61,9876,9878],{"className":9877},[68],[70,9879,9880],{"xmlns":72},[74,9881,9882,9889],{},[77,9883,9884,9887],{},[1817,9885,9886],{}," ",[1817,9888,9886],{},[102,9890,9891],{"encoding":104},"\\,\\,",[61,9893,9895],{"className":9894,"ariaHidden":110},[109],[61,9896,9898,9902,9906],{"className":9897},[114],[61,9899],{"className":9900,"style":9901},[118],"height:0em;",[61,9903],{"className":9904,"style":9905},[543],"margin-right:0.1667em;",[61,9907],{"className":9908,"style":9905},[543],[50,9910,9911],{},"dt",[61,9913,9915,9930],{"className":9914},[64],[61,9916,9918],{"className":9917},[68],[70,9919,9920],{"xmlns":72},[74,9921,9922,9928],{},[77,9923,9924,9926],{},[1817,9925,9886],{},[1817,9927,9886],{},[102,9929,9891],{"encoding":104},[61,9931,9933],{"className":9932,"ariaHidden":110},[109],[61,9934,9936,9939,9942],{"className":9935},[114],[61,9937],{"className":9938,"style":9901},[118],[61,9940],{"className":9941,"style":9905},[543],[61,9943],{"className":9944,"style":9905},[543],"利用其他不显含时间的量",[61,9947,9952],{"className":9948,"title":9950,"style":9951},[9949],"katex-error","ParseError: KaTeX parse error: Can't use function '$' in math mode at position 5: \\,\\,$̲$\\pmb{\\omega}$$…","color:#cc0000","\\,\\,$$\\pmb{\\omega}$$\\,\\,","​来进行表示",[14,9955,9956,9957,9960],{},"​\t\t\t\t\t\t这与有心力场中轨道微分方程 ",[9818,9958,9959],{},"Binet公式","的思想相同",[24,9962,9963,9966,9969],{},[14,9964,9965],{},"沿运动方向：切向加速度",[14,9967,9968],{},"垂直运动方向：向心加速度",[61,9970,9972],{"className":9971},[421],[61,9973,9975,10031],{"className":9974},[64],[61,9976,9978],{"className":9977},[68],[70,9979,9980],{"xmlns":72,"display":430},[74,9981,9982,10028],{},[77,9983,9984,9987,9991,9993,10003,10011,10013,10019],{},[1817,9985,9986],{},"合并在一个式子里即",[89,9988,9989],{"style":91},[85,9990,228],{},[442,9992,444],{},[80,9994,9995,10001],{},[8417,9996,9997,9999],{},[85,9998,58],{},[6846,10000,8427],{},[85,10002,3494],{},[89,10004,10005],{"style":91},[1366,10006,10007,10009],{"accent":110},[85,10008,52],{},[442,10010,1372],{},[442,10012,472],{},[1366,10014,10015,10017],{"accent":110},[85,10016,9107],{},[442,10018,3037],{},[89,10020,10021],{"style":91},[1366,10022,10023,10026],{"accent":110},[85,10024,10025],{},"τ",[442,10027,1372],{},[102,10029,10030],{"encoding":104},"合并在一个式子里即\\pmb{a}=\\frac{v^2}{\\rho}\\pmb{\\hat{r}}+\\ddot{s}\\pmb{\\hat{\\tau}}",[61,10032,10034,10059,10200],{"className":10033,"ariaHidden":110},[109],[61,10035,10037,10041,10044,10050,10053,10056],{"className":10036},[114],[61,10038],{"className":10039,"style":10040},[118],"height:0.6833em;",[61,10042,9986],{"className":10043},[123,1885],[61,10045,10047],{"className":10046,"style":200},[123],[61,10048,228],{"className":10049},[123,167],[61,10051],{"className":10052,"style":544},[543],[61,10054,444],{"className":10055},[548],[61,10057],{"className":10058,"style":544},[543],[61,10060,10062,10066,10157,10191,10194,10197],{"className":10061},[114],[61,10063],{"className":10064,"style":10065},[118],"height:2.3715em;vertical-align:-0.8804em;",[61,10067,10069,10072,10154],{"className":10068},[123],[61,10070],{"className":10071},[127,128],[61,10073,10075],{"className":10074},[80],[61,10076,10078,10146],{"className":10077},[135,136],[61,10079,10081,10143],{"className":10080},[140],[61,10082,10085,10096,10104],{"className":10083,"style":10084},[144],"height:1.4911em;",[61,10086,10087,10090],{"style":580},[61,10088],{"className":10089,"style":153},[152],[61,10091,10093],{"className":10092},[123],[61,10094,3494],{"className":10095},[123,167],[61,10097,10098,10101],{"style":173},[61,10099],{"className":10100,"style":153},[152],[61,10102],{"className":10103,"style":181},[180],[61,10105,10106,10109],{"style":604},[61,10107],{"className":10108,"style":153},[152],[61,10110,10112],{"className":10111},[123],[61,10113,10115,10118],{"className":10114},[123],[61,10116,58],{"className":10117,"style":333},[123,167],[61,10119,10121],{"className":10120},[8715],[61,10122,10124],{"className":10123},[135],[61,10125,10127],{"className":10126},[140],[61,10128,10131],{"className":10129,"style":10130},[144],"height:0.8141em;",[61,10132,10134,10137],{"style":10133},"top:-3.063em;margin-right:0.05em;",[61,10135],{"className":10136,"style":6445},[152],[61,10138,10140],{"className":10139},[157,158,159,160],[61,10141,8427],{"className":10142},[123,160],[61,10144,209],{"className":10145},[208],[61,10147,10149],{"className":10148},[140],[61,10150,10152],{"className":10151,"style":1127},[144],[61,10153],{},[61,10155],{"className":10156},[222,128],[61,10158,10160],{"className":10159,"style":200},[123],[61,10161,10163],{"className":10162},[123,1391],[61,10164,10166],{"className":10165},[135],[61,10167,10169],{"className":10168},[140],[61,10170,10172,10180],{"className":10171,"style":407},[144],[61,10173,10174,10177],{"style":1403},[61,10175],{"className":10176,"style":153},[152],[61,10178,52],{"className":10179,"style":204},[123,167],[61,10181,10182,10185],{"style":1403},[61,10183],{"className":10184,"style":153},[152],[61,10186,10188],{"className":10187,"style":1603},[1418],[61,10189,1372],{"className":10190},[123],[61,10192],{"className":10193,"style":644},[543],[61,10195,472],{"className":10196},[648],[61,10198],{"className":10199,"style":644},[543],[61,10201,10203,10206,10237],{"className":10202},[114],[61,10204],{"className":10205,"style":407},[118],[61,10207,10209],{"className":10208},[123,1391],[61,10210,10212],{"className":10211},[135],[61,10213,10215],{"className":10214},[140],[61,10216,10218,10226],{"className":10217,"style":2751},[144],[61,10219,10220,10223],{"style":1403},[61,10221],{"className":10222,"style":153},[152],[61,10224,9107],{"className":10225},[123,167],[61,10227,10228,10231],{"style":1403},[61,10229],{"className":10230,"style":153},[152],[61,10232,10234],{"className":10233,"style":1603},[1418],[61,10235,3037],{"className":10236},[123],[61,10238,10240],{"className":10239,"style":200},[123],[61,10241,10243],{"className":10242},[123,1391],[61,10244,10246],{"className":10245},[135],[61,10247,10249],{"className":10248},[140],[61,10250,10252,10261],{"className":10251,"style":407},[144],[61,10253,10254,10257],{"style":1403},[61,10255],{"className":10256,"style":153},[152],[61,10258,10025],{"className":10259,"style":10260},[123,167],"margin-right:0.1132em;",[61,10262,10263,10266],{"style":1403},[61,10264],{"className":10265,"style":153},[152],[61,10267,10269],{"className":10268,"style":1419},[1418],[61,10270,1372],{"className":10271},[123],[14,10273,10274,10313],{},[61,10275,10277,10295],{"className":10276},[64],[61,10278,10280],{"className":10279},[68],[70,10281,10282],{"xmlns":72},[74,10283,10284,10292],{},[77,10285,10286,10288,10290],{},[1817,10287,9886],{},[1817,10289,9886],{},[1817,10291,9886],{},[102,10293,10294],{"encoding":104},"\\,\\,\\,",[61,10296,10298],{"className":10297,"ariaHidden":110},[109],[61,10299,10301,10304,10307,10310],{"className":10300},[114],[61,10302],{"className":10303,"style":9901},[118],[61,10305],{"className":10306,"style":9905},[543],[61,10308],{"className":10309,"style":9905},[543],[61,10311],{"className":10312,"style":9905},[543],"另外的应用——软绳坐标（在约束中再提）",[349,10315,10317],{"id":10316},"二对于不同参照系下同一视角下的描述","（二）对于不同参照系下同一“视角下的描述”",[42,10319,10320],{"id":10320},"参考系",[14,10322,10323],{},"相对于任意参考系，空间是非均匀且各向异性的，即某个物体与其他物体没有相互作用，它在空间中的不同位置和不同指向在力学意义上是不等价的.同样，一般情况下任意参考系中的时间也是非均匀的，即不同时刻也是不等价的.显然，时间和空间的这些性质使力学现象的描述变得复杂.",[14,10325,10326],{},"然而，似乎总是存在某种参考系，空间相对它是均匀的、各向同性的，时间相对于它是均匀的——这样的参考系称为惯性参考系。",[14,10328,10330],{"align":10329},"right","————上述两段摘自Landau力学",[42,10332,10333],{"id":10333},"伽利略变换",[14,10335,10336],{},"对于两个惯性参考系之间的变换，",[14,10338,10339,10470],{},[61,10340,10342,10378],{"className":10341},[64],[61,10343,10345],{"className":10344},[68],[70,10346,10347],{"xmlns":72},[74,10348,10349,10375],{},[77,10350,10351,10361,10363,10367,10369,10373],{},[89,10352,10353],{"style":91},[8417,10354,10355,10357],{},[85,10356,52],{},[442,10358,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},"0em","′",[442,10362,444],{},[89,10364,10365],{"style":91},[85,10366,52],{},[442,10368,472],{},[89,10370,10371],{"style":91},[85,10372,364],{},[85,10374,100],{},[102,10376,10377],{"encoding":104},"\\pmb{r'}=\\pmb{r}+\\pmb{u}t",[61,10379,10381,10432,10454],{"className":10380,"ariaHidden":110},[109],[61,10382,10384,10388,10423,10426,10429],{"className":10383},[114],[61,10385],{"className":10386,"style":10387},[118],"height:0.7519em;",[61,10389,10391],{"className":10390,"style":200},[123],[61,10392,10394,10397],{"className":10393},[123],[61,10395,52],{"className":10396,"style":204},[123,167],[61,10398,10400],{"className":10399},[8715],[61,10401,10403],{"className":10402},[135],[61,10404,10406],{"className":10405},[140],[61,10407,10409],{"className":10408,"style":10387},[144],[61,10410,10411,10414],{"style":10133},[61,10412],{"className":10413,"style":6445},[152],[61,10415,10417],{"className":10416},[157,158,159,160],[61,10418,10420],{"className":10419},[123,160],[61,10421,10360],{"className":10422},[123,160],[61,10424],{"className":10425,"style":544},[543],[61,10427,444],{"className":10428},[548],[61,10430],{"className":10431,"style":544},[543],[61,10433,10435,10439,10445,10448,10451],{"className":10434},[114],[61,10436],{"className":10437,"style":10438},[118],"height:0.6667em;vertical-align:-0.0833em;",[61,10440,10442],{"className":10441,"style":200},[123],[61,10443,52],{"className":10444,"style":204},[123,167],[61,10446],{"className":10447,"style":644},[543],[61,10449,472],{"className":10450},[648],[61,10452],{"className":10453,"style":644},[543],[61,10455,10457,10461,10467],{"className":10456},[114],[61,10458],{"className":10459,"style":10460},[118],"height:0.6151em;",[61,10462,10464],{"className":10463,"style":200},[123],[61,10465,364],{"className":10466},[123,167],[61,10468,100],{"className":10469},[123,167],[61,10471,10473,10495],{"className":10472},[64],[61,10474,10476],{"className":10475},[68],[70,10477,10478],{"xmlns":72},[74,10479,10480,10492],{},[77,10481,10482,10488,10490],{},[8417,10483,10484,10486],{},[85,10485,100],{},[442,10487,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,10489,444],{},[85,10491,100],{},[102,10493,10494],{"encoding":104},"t'=t",[61,10496,10498,10545],{"className":10497,"ariaHidden":110},[109],[61,10499,10501,10504,10536,10539,10542],{"className":10500},[114],[61,10502],{"className":10503,"style":10387},[118],[61,10505,10507,10510],{"className":10506},[123],[61,10508,100],{"className":10509},[123,167],[61,10511,10513],{"className":10512},[8715],[61,10514,10516],{"className":10515},[135],[61,10517,10519],{"className":10518},[140],[61,10520,10522],{"className":10521,"style":10387},[144],[61,10523,10524,10527],{"style":10133},[61,10525],{"className":10526,"style":6445},[152],[61,10528,10530],{"className":10529},[157,158,159,160],[61,10531,10533],{"className":10532},[123,160],[61,10534,10360],{"className":10535},[123,160],[61,10537],{"className":10538,"style":544},[543],[61,10540,444],{"className":10541},[548],[61,10543],{"className":10544,"style":544},[543],[61,10546,10548,10551],{"className":10547},[114],[61,10549],{"className":10550,"style":10460},[118],[61,10552,100],{"className":10553},[123,167],[14,10555,10556],{},"​两个式子即代表了两个惯性参照系的坐标与时间关系，后者为经典力学中的绝对时间假设",[14,10558,10559],{},"对上式进行求导，得到了两个坐标系的速度变换公式",[61,10561,10563],{"className":10562},[421],[61,10564,10566,10598],{"className":10565},[64],[61,10567,10569],{"className":10568},[68],[70,10570,10571],{"xmlns":72,"display":430},[74,10572,10573,10595],{},[77,10574,10575,10583,10585,10589,10591],{},[89,10576,10577],{"style":91},[8417,10578,10579,10581],{},[85,10580,58],{},[442,10582,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,10584,444],{},[89,10586,10587],{"style":91},[85,10588,58],{},[442,10590,472],{},[89,10592,10593],{"style":91},[85,10594,364],{},[102,10596,10597],{"encoding":104},"\\pmb{v'}=\\pmb{v}+\\pmb{u}",[61,10599,10601,10652,10673],{"className":10600,"ariaHidden":110},[109],[61,10602,10604,10608,10643,10646,10649],{"className":10603},[114],[61,10605],{"className":10606,"style":10607},[118],"height:0.8019em;",[61,10609,10611],{"className":10610,"style":200},[123],[61,10612,10614,10617],{"className":10613},[123],[61,10615,58],{"className":10616,"style":333},[123,167],[61,10618,10620],{"className":10619},[8715],[61,10621,10623],{"className":10622},[135],[61,10624,10626],{"className":10625},[140],[61,10627,10629],{"className":10628,"style":10607},[144],[61,10630,10631,10634],{"style":8728},[61,10632],{"className":10633,"style":6445},[152],[61,10635,10637],{"className":10636},[157,158,159,160],[61,10638,10640],{"className":10639},[123,160],[61,10641,10360],{"className":10642},[123,160],[61,10644],{"className":10645,"style":544},[543],[61,10647,444],{"className":10648},[548],[61,10650],{"className":10651,"style":544},[543],[61,10653,10655,10658,10664,10667,10670],{"className":10654},[114],[61,10656],{"className":10657,"style":10438},[118],[61,10659,10661],{"className":10660,"style":200},[123],[61,10662,58],{"className":10663,"style":333},[123,167],[61,10665],{"className":10666,"style":644},[543],[61,10668,472],{"className":10669},[648],[61,10671],{"className":10672,"style":644},[543],[61,10674,10676,10679],{"className":10675},[114],[61,10677],{"className":10678,"style":2195},[118],[61,10680,10682],{"className":10681,"style":200},[123],[61,10683,364],{"className":10684},[123,167],[14,10686,10687],{},"伽利略相对性原理也可以表述为：力学运动方程在伽利略变换下具有不变性（形式不变）",[42,10689,10690],{"id":10690},"在不同坐标系下描述物体的运动",[358,10692,10694],{"id":10693},"_1两个互作平动的参照系之间的变换","1.两个互作平动的参照系之间的变换",[14,10696,10697,10698,10823],{},"互作平动，但是未必相对运动是匀速运动",[61,10699,10701,10734],{"className":10700},[64],[61,10702,10704],{"className":10703},[68],[70,10705,10706],{"xmlns":72},[74,10707,10708,10732],{},[77,10709,10710,10718,10720,10724,10726,10730],{},[89,10711,10712],{"style":91},[8417,10713,10714,10716],{},[85,10715,52],{},[442,10717,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,10719,444],{},[89,10721,10722],{"style":91},[85,10723,52],{},[442,10725,472],{},[89,10727,10728],{"style":91},[85,10729,364],{},[85,10731,100],{},[102,10733,10377],{"encoding":104},[61,10735,10737,10787,10808],{"className":10736,"ariaHidden":110},[109],[61,10738,10740,10743,10778,10781,10784],{"className":10739},[114],[61,10741],{"className":10742,"style":10387},[118],[61,10744,10746],{"className":10745,"style":200},[123],[61,10747,10749,10752],{"className":10748},[123],[61,10750,52],{"className":10751,"style":204},[123,167],[61,10753,10755],{"className":10754},[8715],[61,10756,10758],{"className":10757},[135],[61,10759,10761],{"className":10760},[140],[61,10762,10764],{"className":10763,"style":10387},[144],[61,10765,10766,10769],{"style":10133},[61,10767],{"className":10768,"style":6445},[152],[61,10770,10772],{"className":10771},[157,158,159,160],[61,10773,10775],{"className":10774},[123,160],[61,10776,10360],{"className":10777},[123,160],[61,10779],{"className":10780,"style":544},[543],[61,10782,444],{"className":10783},[548],[61,10785],{"className":10786,"style":544},[543],[61,10788,10790,10793,10799,10802,10805],{"className":10789},[114],[61,10791],{"className":10792,"style":10438},[118],[61,10794,10796],{"className":10795,"style":200},[123],[61,10797,52],{"className":10798,"style":204},[123,167],[61,10800],{"className":10801,"style":644},[543],[61,10803,472],{"className":10804},[648],[61,10806],{"className":10807,"style":644},[543],[61,10809,10811,10814,10820],{"className":10810},[114],[61,10812],{"className":10813,"style":10460},[118],[61,10815,10817],{"className":10816,"style":200},[123],[61,10818,364],{"className":10819},[123,167],[61,10821,100],{"className":10822},[123,167],"​ ✘",[14,10825,10826],{},"下面给出变换公式及其推导",[61,10828,10830],{"className":10829},[421],[61,10831,10833,10865],{"className":10832},[64],[61,10834,10836],{"className":10835},[68],[70,10837,10838],{"xmlns":72,"display":430},[74,10839,10840,10862],{},[77,10841,10842,10850,10852,10856,10858],{},[89,10843,10844],{"style":91},[8417,10845,10846,10848],{},[85,10847,52],{},[442,10849,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,10851,444],{},[89,10853,10854],{"style":91},[85,10855,52],{},[442,10857,472],{},[89,10859,10860],{"style":91},[85,10861,3494],{},[102,10863,10864],{"encoding":104},"\\pmb{r'}=\\pmb{r}+\\pmb{\\rho}",[61,10866,10868,10918,10939],{"className":10867,"ariaHidden":110},[109],[61,10869,10871,10874,10909,10912,10915],{"className":10870},[114],[61,10872],{"className":10873,"style":10607},[118],[61,10875,10877],{"className":10876,"style":200},[123],[61,10878,10880,10883],{"className":10879},[123],[61,10881,52],{"className":10882,"style":204},[123,167],[61,10884,10886],{"className":10885},[8715],[61,10887,10889],{"className":10888},[135],[61,10890,10892],{"className":10891},[140],[61,10893,10895],{"className":10894,"style":10607},[144],[61,10896,10897,10900],{"style":8728},[61,10898],{"className":10899,"style":6445},[152],[61,10901,10903],{"className":10902},[157,158,159,160],[61,10904,10906],{"className":10905},[123,160],[61,10907,10360],{"className":10908},[123,160],[61,10910],{"className":10911,"style":544},[543],[61,10913,444],{"className":10914},[548],[61,10916],{"className":10917,"style":544},[543],[61,10919,10921,10924,10930,10933,10936],{"className":10920},[114],[61,10922],{"className":10923,"style":10438},[118],[61,10925,10927],{"className":10926,"style":200},[123],[61,10928,52],{"className":10929,"style":204},[123,167],[61,10931],{"className":10932,"style":644},[543],[61,10934,472],{"className":10935},[648],[61,10937],{"className":10938,"style":644},[543],[61,10940,10942,10945],{"className":10941},[114],[61,10943],{"className":10944,"style":3989},[118],[61,10946,10948],{"className":10947,"style":200},[123],[61,10949,3494],{"className":10950},[123,167],[61,10952,10954],{"className":10953},[421],[61,10955,10957,11073],{"className":10956},[64],[61,10958,10960],{"className":10959},[68],[70,10961,10962],{"xmlns":72,"display":430},[74,10963,10964,11070],{},[77,10965,10966,10982,10985,10989,10991,11007,11009,11013,11015,11035,11037,11045,11047,11063,11065],{},[80,10967,10968,10976],{},[77,10969,10970,10972],{},[85,10971,87],{},[89,10973,10974],{"style":91},[85,10975,3494],{},[77,10977,10978,10980],{},[85,10979,87],{},[85,10981,100],{},[442,10983,10984],{},"≜",[89,10986,10987],{"style":91},[85,10988,364],{},[442,10990,365],{"separator":110},[80,10992,10993,11001],{},[77,10994,10995,10997],{},[85,10996,87],{},[89,10998,10999],{"style":91},[85,11000,52],{},[77,11002,11003,11005],{},[85,11004,87],{},[85,11006,100],{},[442,11008,10984],{},[89,11010,11011],{"style":91},[85,11012,58],{},[442,11014,365],{"separator":110},[80,11016,11017,11029],{},[77,11018,11019,11021],{},[85,11020,87],{},[89,11022,11023],{"style":91},[8417,11024,11025,11027],{},[85,11026,52],{},[442,11028,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[77,11030,11031,11033],{},[85,11032,87],{},[85,11034,100],{},[442,11036,10984],{},[89,11038,11039],{"style":91},[8417,11040,11041,11043],{},[85,11042,58],{},[442,11044,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,11046,365],{"separator":110},[80,11048,11049,11057],{},[77,11050,11051,11053],{},[85,11052,87],{},[89,11054,11055],{"style":91},[85,11056,364],{},[77,11058,11059,11061],{},[85,11060,87],{},[85,11062,100],{},[442,11064,10984],{},[89,11066,11067],{"style":91},[85,11068,11069],{},"A",[102,11071,11072],{"encoding":104},"\\frac{d\\pmb{\\rho}}{dt}\\triangleq \\pmb{u},\\frac{d\\pmb{r}}{dt}\\triangleq \\pmb{v},\\frac{d\\pmb{r'}}{dt}\\triangleq \\pmb{v'},\\frac{d\\pmb{u}}{dt}\\triangleq 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assName":12595,"style":6445},[152],[61,12597,12599],{"className":12598},[157,158,159,160],[61,12600,12602],{"className":12601},[123,160],[61,12603,12605,12608],{"className":12604},[123,160],[61,12606,11845],{"className":12607,"style":12195},[123,167,160],[61,12609,12611],{"className":12610},[8715],[61,12612,12614],{"className":12613},[135],[61,12615,12617],{"className":12616},[140],[61,12618,12620],{"className":12619,"style":12344},[144],[61,12621,12622,12625],{"style":12347},[61,12623],{"className":12624,"style":12351},[152],[61,12626,12628],{"className":12627},[157,12355,12356,160],[61,12629,12631],{"className":12630},[123,160],[61,12632,10360],{"className":12633},[123,160],[61,12635,209],{"className":12636},[208],[61,12638,12640],{"className":12639},[140],[61,12641,12643],{"className":12642,"style":12205},[144],[61,12644],{},[61,12646,12463],{"className":12647},[123,1885],[61,12649,12651],{"className":12650,"style":200},[123],[61,12652,11863],{"className":12653,"style":11882},[123,167],[61,12655,12470],{"className":12656},[123,1885],[61,12658,11845],{"className":12659,"style":12195},[123,167],[61,12661,12663],{"className":12662},[123],"’",[61,12665,12667],{"className":12666},[123,1885],"系中不旋转，只伸长",[61,12669,12671],{"className":12670,"style":204},[123,167],"or",[61,12673,12483],{"className":12674},[123,1885],[14,12676,12677],{},"应用上述结论，则有速度变换",[61,12679,12681],{"className":12680},[421],[61,12682,12684,12762],{"className":12683},[64],[61,12685,12687],{"className":12686},[68],[70,12688,12689],{"xmlns":72,"display":430},[74,12690,12691,12759],{},[77,12692,12693,12695,12711,12717,12719,12721,12737,12747,12749,12753,12755],{},[442,12694,6942],{"stretchy":6941},[80,12696,12697,12705],{},[77,12698,12699,12701],{},[85,12700,87],{},[89,12702,12703],{"style":91},[85,12704,52],{},[77,12706,12707,12709],{},[85,12708,87],{},[85,12710,100],{},[12029,12712,12713,12715],{},[442,12714,6956],{"stretchy":6941},[85,12716,11845],{},[442,12718,444],{},[442,12720,6942],{"stretchy":6941},[80,12722,12723,12731],{},[77,12724,12725,12727],{},[85,12726,87],{},[89,12728,12729],{"style":91},[85,12730,52],{},[77,12732,12733,12735],{},[85,12734,87],{},[85,12736,100],{},[12029,12738,12739,12741],{},[442,12740,6956],{"stretchy":6941},[8417,12742,12743,12745],{},[85,12744,11845],{},[442,12746,10360],{"mathvariant":454,"lspace":10359,"rspace":10359},[442,12748,472],{},[89,12750,12751],{"style":91},[85,12752,11900],{},[442,12754,12073],{},[89,12756,12757],{"style":91},[85,12758,52],{},[102,12760,12761],{"encoding":104},"(\\frac{d\\pmb{r}}{dt})_S=(\\frac{d\\pmb{r}}{dt})_{S'}+\\pmb{\\omega}\\times\\pmb{r}",[61,12763,12765,12894,13055,13076],{"className":12764,"ariaHidden":110},[109],[61,12766,12768,12771,12774,12845,12885,12888,12891],{"className":12767},[114],[61,12769],{"className":12770,"style":558},[118],[61,12772,6942],{"className":12773},[127],[61,12775,12777,12780,12842],{"className":12776},[123],[61,12778],{"className":12779},[127,128],[61,12781,12783],{"className":12782},[80],[61,12784,12786,12834],{"className":12785},[135,136],[61,12787,12789,12831],{"className":12788},[140],[61,12790,12792,12806,12814],{"className":12791,"style":577},[144],[61,12793,12794,12797],{"style":580},[61,12795],{"className":12796,"style":153},[152],[61,12798,12800,12803],{"className":12799},[123],[61,12801,87],{"className":12802},[123,167],[61,12804,100],{"className":12805},[123,167],[61,12807,12808,12811],{"style":173},[61,12809],{"className":12810,"style":153},[152],[61,12812],{"className":12813,"style":181},[180],[61,12815,12816,12819],{"style":604},[61,12817],{"className":12818,"style":153},[152],[61,12820,12822,12825],{"className":12821},[123],[61,12823,87],{"className":12824},[123,167],[61,12826,12828],{"className":12827,"style":200},[123],[61,12829,52],{"className":12830,"style":204},[123,167],[61,12832,209],{"className":12833},[208],[61,12835,12837],{"className":12836},[140],[61,12838,12840],{"className":12839,"style":629},[144],[61,12841],{},[61,12843],{"className":12844},[222,128],[61,12846,12848,12851],{"className":12847},[222],[61,12849,6956],{"className":12850},[222],[61,12852,12854],{"className":12853},[8715],[61,12855,12857,12877],{"className":12856},[135,136],[61,12858,12860,12874],{"className":12859},[140],[61,12861,12863],{"className":12862,"style":12182},[144],[61,12864,12865,12868],{"style":12185},[61,12866],{"className":12867,"style":6445},[152],[61,12869,12871],{"className":12870},[157,158,159,160],[61,12872,11845],{"className":12873,"style":12195},[123,167,160],[61,12875,209],{"className":12876},[208],[61,12878,12880],{"className":12879},[140],[61,12881,12883],{"className":12882,"style":12205},[144],[61,12884],{},[61,12886],{"className":12887,"style":544},[543],[61,12889,444],{"className":12890},[548],[61,12892],{"className":12893,"style":544},[543],[61,12895,12897,12900,12903,12974,13046,13049,13052],{"className":12896},[114],[61,12898],{"className":12899,"style":558},[118],[61,12901,6942],{"className":12902},[127],[61,12904,12906,12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）",[14,17950,17951],{},"前情提要：",[14,17953,17954],{},"上面对于运动的描述都是对于单个物体（质点）而言，对于质点系而言，当然可以对每个质点单独进行描述，但是对于质点之间，存在着一定的约束，下面我们讨论有约束关系我们能获得什么：",[349,17956,17958],{"id":17957},"三约束","（三）约束",[14,17960,17961],{},"理想约束\u002F非理想约束，这个等到后面分析力学再详细展开（或者再这里再补充）",[14,17963,17964],{},"这里仅举常用的一些例子，但是会从更数学的角度去处理约束关系，和从物理的角度对比一下，更好的理解运动关联的那些事",[14,17966,17967],{},"eg1:杆模型",[14,17969,17970],{},[228,17971,17974],{"href":17972,"rel":17973},"https:\u002F\u002Fimgse.com\u002Fi\u002FpF1nFKO",[9834],[9836,17975],{"alt":17976,"src":17977},"pF1nFKO.md.jpg","https:\u002F\u002Fs11.ax1x.com\u002F2024\u002F02\u002F06\u002FpF1nFKO.md.jpg",[14,17979,17980,17981,18009,18010,18039,18040,18170],{},"杆模型这里只关注两个端点的约束关系，杆长为",[61,17982,17984,17997],{"className":17983},[64],[61,17985,17987],{"className":17986},[68],[70,17988,17989],{"xmlns":72},[74,17990,17991,17995],{},[77,17992,17993],{},[85,17994,9078],{},[102,17996,9078],{"encoding":104},[61,17998,18000],{"className":17999,"ariaHidden":110},[109],[61,18001,18003,18006],{"className":18002},[114],[61,18004],{"className":18005,"style":407},[118],[61,18007,9078],{"className":18008,"style":9156},[123,167],",选取一个原点为",[61,18011,18013,18027],{"className":18012},[64],[61,18014,18016],{"className":18015},[68],[70,18017,18018],{"xmlns":72},[74,18019,18020,18025],{},[77,18021,18022],{},[85,18023,18024],{},"O",[102,18026,18024],{"encoding":104},[61,18028,18030],{"className":18029,"ariaHidden":110},[109],[61,18031,18033,18036],{"className":18032},[114],[61,18034],{"className":18035,"style":10040},[118],[61,18037,18024],{"className":18038,"style":204},[123,167],",则此时描述两个质点的运动由",[61,18041,18043,18072],{"className":18042},[64],[61,18044,18046],{"className":18045},[68],[70,18047,18048],{"xmlns":72},[74,18049,18050,18069],{},[77,18051,18052],{},[89,18053,18054,18061,18063],{"style":91},[12029,18055,18056,18058],{},[85,18057,52],{},[6846,18059,18060],{},"1",[1817,18062,9886],{},[12029,18064,18065,18067],{},[85,18066,52],{},[6846,18068,8427],{},[102,18070,18071],{"encoding":104},"\\pmb{r_1\\,r_2}",[61,18073,18075],{"className":18074,"ariaHidden":110},[109],[61,18076,18078,18082],{"className":18077},[114],[61,18079],{"className":18080,"style":18081},[118],"height:0.5806em;vertical-align:-0.15em;",[61,18083,18085,18127,18130],{"className":18084,"style":200},[123],[61,18086,18088,18091],{"className":18087},[123],[61,18089,52],{"className":18090,"style":204},[123,167],[61,18092,18094],{"className":18093},[8715],[61,18095,18097,18119],{"className":18096},[135,136],[61,18098,18100,18116],{"className":18099},[140],[61,18101,18104],{"className":18102,"style":18103},[144],"height:0.3011em;",[61,18105,18107,18110],{"style":18106},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[61,18108],{"className":18109,"style":6445},[152],[61,18111,18113],{"className":18112},[157,158,159,160],[61,18114,18060],{"className":18115},[123,160],[61,18117,209],{"className":18118},[208],[61,18120,18122],{"className":18121},[140],[61,18123,18125],{"className":18124,"style":12205},[144],[61,18126],{},[61,18128],{"className":18129,"style":9905},[543],[61,18131,18133,18136],{"className":18132},[123],[61,18134,52],{"className":18135,"style":204},[123,167],[61,18137,18139],{"className":18138},[8715],[61,18140,18142,18162],{"className":18141},[135,136],[61,18143,18145,18159],{"className":18144},[140],[61,18146,18148],{"className":18147,"style":18103},[144],[61,18149,18150,18153],{"style":18106},[61,18151],{"className":18152,"style":6445},[152],[61,18154,18156],{"className":18155},[157,158,159,160],[61,18157,8427],{"className":18158},[123,160],[61,18160,209],{"className":18161},[208],[61,18163,18165],{"className":18164},[140],[61,18166,18168],{"className":18167,"style":12205},[144],[61,18169],{},"来决定",[14,18172,18173,18174],{},"那这两个质点（两个端点）有什么约束关系——很简单，",[61,18175,18177,18218],{"className":18176},[64],[61,18178,18180],{"className":18179},[68],[70,18181,18182],{"xmlns":72},[74,18183,18184,18215],{},[77,18185,18186,18189,18209,18211,18213],{},[85,18187,18188],{"mathvariant":454},"∣",[77,18190,18191,18199,18201],{},[89,18192,18193],{"style":91},[12029,18194,18195,18197],{},[85,18196,52],{},[6846,18198,18060],{},[442,18200,6945],{},[89,18202,18203],{"style":91},[12029,18204,18205,18207],{},[85,18206,52],{},[6846,18208,8427],{},[85,18210,18188],{"mathvariant":454},[442,18212,444],{},[85,18214,9078],{},[102,18216,18217],{"encoding":104},"|{\\pmb{r_1}-\\pmb{r_2}}| = l",[61,18219,18221,18340],{"className":18220,"ariaHidden":110},[109],[61,18222,18224,18227,18230,18328,18331,18334,18337],{"className":18223},[114],[61,18225],{"className":18226,"style":7721},[118],[61,18228,18188],{"className":18229},[123],[61,18231,18233,18276,18279,18282,18285],{"className":18232},[123],[61,18234,18236],{"className":18235,"style":200},[123],[61,18237,18239,18242],{"className":18238},[123],[61,18240,52],{"className":18241,"style":204},[123,167],[61,18243,18245],{"className":18244},[8715],[61,18246,18248,18268],{"className":18247},[135,136],[61,18249,18251,18265],{"className":18250},[140],[61,18252,18254],{"className":18253,"style":18103},[144],[61,18255,18256,18259],{"style":18106},[61,18257],{"className":18258,"style":6445},[152],[61,18260,18262],{"className":18261},[157,158,159,160],[61,18263,18060],{"className":18264},[123,160],[61,18266,209],{"className":18267},[208],[61,18269,18271],{"className":18270},[140],[61,18272,18274],{"className":18273,"style":12205},[144],[61,18275],{},[61,18277],{"className":18278,"style":644},[543],[61,18280,6945],{"className":18281},[648],[61,18283],{"className":18284,"style":644},[543],[61,18286,18288],{"className":18287,"style":200},[123],[61,18289,18291,18294],{"className":18290},[123],[61,18292,52],{"className":18293,"style":204},[123,167],[61,18295,18297],{"className":18296},[8715],[61,18298,18300,18320],{"className":18299},[135,136],[61,18301,18303,18317],{"className":18302},[140],[61,18304,18306],{"className":18305,"style":18103},[144],[61,18307,18308,18311],{"style":18106},[61,18309],{"className":18310,"style":6445},[152],[61,18312,18314],{"className":18313},[157,158,159,160],[61,18315,8427],{"className":18316},[123,160],[61,18318,209],{"className":18319},[208],[61,18321,18323],{"className":18322},[140],[61,18324,18326],{"className":18325,"style":12205},[144],[61,18327],{},[61,18329,18188],{"className":18330},[123],[61,18332],{"className":18333,"style":544},[543],[61,18335,444],{"className":18336},[548],[61,18338],{"className":18339,"style":544},[543],[61,18341,18343,18346],{"className":18342},[114],[61,18344],{"className":18345,"style":407},[118],[61,18347,9078],{"className":18348,"style":9156},[123,167],[14,18350,18351,18352],{},"但是操作起来不是那么方便，于是上式改写为",[61,18353,18355,18401],{"className":18354},[64],[61,18356,18358],{"className":18357},[68],[70,18359,18360],{"xmlns":72},[74,18361,18362,18398],{},[77,18363,18364,18366,18374,18376,18384,18390,18392],{},[442,18365,6942],{"stretchy":6941},[89,18367,18368],{"style":91},[12029,18369,18370,18372],{},[85,18371,52],{},[6846,18373,18060],{},[442,18375,6945],{},[89,18377,18378],{"style":91},[12029,18379,18380,18382],{},[85,18381,52],{},[6846,18383,8427],{},[8417,18385,18386,18388],{},[442,18387,6956],{"stretchy":6941},[6846,18389,8427],{},[442,18391,444],{},[8417,18393,18394,18396],{},[85,18395,9078],{},[6846,18397,8427],{},[102,18399,18400],{"encoding":104},"(\\pmb{r_1}-\\pmb{r_2})^2=l^2",[61,18402,18404,18465,18553],{"className":18403,"ariaHidden":110},[109],[61,18405,18407,18410,18413,18456,18459,18462],{"className":18406},[114],[61,18408],{"className":18409,"style":7721},[118],[61,18411,6942],{"className":18412},[127],[61,18414,18416],{"className":18415,"style":200},[123],[61,18417,18419,18422],{"className":18418},[123],[61,18420,52],{"className":18421,"style":204},[123,167],[61,18423,18425],{"className":18424},[8715],[61,18426,18428,18448],{"className":18427},[135,136],[61,18429,18431,18445],{"className":18430},[140],[61,18432,18434],{"className":18433,"style":18103},[144],[61,18435,18436,18439],{"style":18106},[61,18437],{"className":18438,"style":6445},[152],[61,18440,18442],{"className":18441},[157,158,159,160],[61,18443,18060],{"className":18444},[123,160],[61,18446,209],{"className":18447},[208],[61,18449,18451],{"className":18450},[140],[61,18452,18454],{"className":18453,"style":12205},[144],[61,18455],{},[61,18457],{"className":18458,"style":644},[543],[61,18460,6945],{"className":18461},[648],[61,18463],{"className":18464,"style":644},[543],[61,18466,18468,18472,18515,18544,18547,18550],{"className":18467},[114],[61,18469],{"className":18470,"style":18471},[118],"height:1.0641em;vertical-align:-0.25em;",[61,18473,18475],{"className":18474,"style":200},[123],[61,18476,18478,18481],{"className":18477},[123],[61,18479,52],{"className":18480,"style":204},[123,167],[61,18482,18484],{"className":18483},[8715],[61,18485,18487,18507],{"className":18486},[135,136],[61,18488,18490,18504],{"className":18489},[140],[61,18491,18493],{"className":18492,"style":18103},[144],[61,18494,18495,18498],{"style":18106},[61,18496],{"className":18497,"style":6445},[152],[61,18499,18501],{"className":18500},[157,158,159,160],[61,18502,8427],{"className":18503},[123,160],[61,18505,209],{"className":18506},[208],[61,18508,18510],{"className":18509},[140],[61,18511,18513],{"className":18512,"style":12205},[144],[61,18514],{},[61,18516,18518,18521],{"className":18517},[222],[61,18519,6956],{"className":18520},[222],[61,18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540,"style":7721},[118],[61,20542,6942],{"className":20543},[127],[61,20545,20547],{"className":20546,"style":200},[123],[61,20548,20550,20553],{"className":20549},[123],[61,20551,58],{"className":20552,"style":333},[123,167],[61,20554,20556],{"className":20555},[8715],[61,20557,20559,20579],{"className":20558},[135,136],[61,20560,20562,20576],{"className":20561},[140],[61,20563,20565],{"className":20564,"style":18103},[144],[61,20566,20567,20570],{"style":19507},[61,20568],{"className":20569,"style":6445},[152],[61,20571,20573],{"className":20572},[157,158,159,160],[61,20574,18060],{"className":20575},[123,160],[61,20577,209],{"className":20578},[208],[61,20580,20582],{"className":20581},[140],[61,20583,20585],{"className":20584,"style":12205},[144],[61,20586],{},[61,20588],{"className":20589,"style":644},[543],[61,20591,6945],{"className":20592},[648],[61,20594],{"className":20595,"style":644},[543],[61,20597,20599,20602,20645,20648,20651,20654],{"className":20598},[114],[61,20600],{"className":20601,"style":7721},[118],[61,20603,20605],{"className":20604,"style":200},[123],[61,20606,20608,20611],{"className":20607},[123],[61,20609,58],{"className":20610,"style":333},[123,167],[61,20612,20614],{"className":20613},[8715],[61,20615,20617,20637],{"className":20616},[135,136],[61,20618,20620,20634],{"className":20619},[140],[61,20621,20623],{"className":20622,"style":18103},[144],[61,20624,20625,20628],{"style":19507},[61,20626],{"className":20627,"style":6445},[152],[61,20629,20631],{"className":20630},[157,158,159,160],[61,20632,8427],{"className":20633},[123,160],[61,20635,209],{"className":20636},[208],[61,20638,20640],{"className":20639},[140],[61,20641,20643],{"className":20642,"style":12205},[144],[61,20644],{},[61,20646,6956],{"className":20647},[222],[61,20649],{"className":20650,"style":544},[543],[61,20652,444],{"className":20653},[548],[61,20655],{"className":20656,"style":544},[543],[61,20658,20660,20663],{"className":20659},[114],[61,20661],{"className":20662,"style":20336},[118],[61,20664,20666],{"className":20665,"style":200},[123],[61,20667,447],{"className":20668},[123],[14,20670,20671,20672,209],{},"这句话代表了什么",[61,20673,20675,20714],{"className":20674},[64],[61,20676,20678],{"className":20677},[68],[70,20679,20680],{"xmlns":72},[74,20681,20682,20711],{},[77,20683,20684,20686,20694,20696,20704,20707],{},[442,20685,6610],{},[89,20687,20688],{"style":91},[12029,20689,20690,20692],{},[85,20691,52],{},[6846,20693,18060],{},[442,20695,6945],{},[89,20697,20698],{"style":91},[12029,20699,20700,20702],{},[85,20701,52],{},[6846,20703,8427],{},[1817,20705,20706],{},"记为",[89,20708,20709],{"style":91},[85,20710,9078],{},[102,20712,20713],{"encoding":104},"\\longrightarrow\\pmb{r_1}-\\pmb{r_2}记为\\pmb{l}",[61,20715,20717,20729,20788],{"className":20716,"ariaHidden":110},[109],[61,20718,20720,20723,20726],{"className":20719},[114],[61,20721],{"className":20722,"style":6623},[118],[61,20724,6610],{"className":20725},[548],[61,20727],{"className":20728,"style":544},[543],[61,20730,20732,20736,20779,20782,20785],{"className":20731},[114],[61,20733],{"className":20734,"style":20735},[118],"height:0.7333em;vertical-align:-0.15em;",[61,20737,20739],{"className":20738,"style":200},[123],[61,20740,20742,20745],{"className":20741},[123],[61,20743,52],{"className":20744,"style":204},[123,167],[61,20746,20748],{"className":20747},[8715],[61,20749,20751,20771],{"className":20750},[135,136],[61,20752,20754,20768],{"className":20753},[140],[61,20755,20757],{"className":20756,"style":18103},[144],[61,20758,20759,20762],{"style":18106},[61,20760],{"className":20761,"style":6445},[152],[61,20763,20765],{"className":20764},[157,158,159,160],[61,20766,18060],{"className":20767},[123,160],[61,20769,209],{"className":20770},[208],[61,20772,20774],{"className":20773},[140],[61,20775,20777],{"className":20776,"style":12205},[144],[61,20778],{},[61,20780],{"className":20781,"style":644},[543],[61,20783,6945],{"className":20784},[648],[61,20786],{"className":20787,"style":644},[543],[61,20789,20791,20795,20838,20841],{"className":20790},[114],[61,20792],{"className":20793,"style":20794},[118],"height:0.8444em;vertical-align:-0.15em;",[61,20796,20798],{"className":20797,"style":200},[123],[61,20799,20801,20804],{"className":20800},[123],[61,20802,52],{"className":20803,"style":204},[123,167],[61,20805,20807],{"className":20806},[8715],[61,20808,20810,20830],{"className":20809},[135,136],[61,20811,20813,20827],{"className":20812},[140],[61,20814,20816],{"className":20815,"style":18103},[144],[61,20817,20818,20821],{"style":18106},[61,20819],{"className":20820,"style":6445},[152],[61,20822,20824],{"className":20823},[157,158,159,160],[61,20825,8427],{"className":20826},[123,160],[61,20828,209],{"className":20829},[208],[61,20831,20833],{"className":20832},[140],[61,20834,20836],{"className":20835,"style":12205},[144],[61,20837],{},[61,20839,20706],{"className":20840},[123,1885],[61,20842,20844],{"className":20843,"style":200},[123],[61,20845,9078],{"className":20846,"style":9156},[123,167],[14,20848,20849,20850],{},"上式化为",[61,20851,20853,20895],{"className":20852},[64],[61,20854,20856],{"className":20855},[68],[70,20857,20858],{"xmlns":72},[74,20859,20860,20892],{},[77,20861,20862,20866,20868,20876,20878,20882,20884],{},[89,20863,20864],{"style":91},[85,20865,9078],{},[442,20867,6856],{},[89,20869,20870],{"style":91},[12029,20871,20872,20874],{},[85,20873,58],{},[6846,20875,18060],{},[442,20877,444],{},[89,20879,20880],{"style":91},[85,20881,9078],{},[442,20883,6856],{},[89,20885,20886],{"style":91},[12029,20887,20888,20890],{},[85,20889,58],{},[6846,20891,8427],{},[102,20893,20894],{"encoding":104},"\\pmb{l}\\cdot\\pmb{v_1}=\\pmb{l}\\cdot\\pmb{v_2}",[61,20896,20898,20919,20977,20998],{"className":20897,"ariaHidden":110},[109],[61,20899,20901,20904,20910,20913,20916],{"className":20900},[114],[61,20902],{"className":20903,"style":407},[118],[61,20905,20907],{"className":20906,"style":200},[123],[61,20908,9078],{"className":20909,"style":9156},[123,167],[61,20911],{"className":20912,"style":644},[543],[61,20914,6856],{"className":20915},[648],[61,20917],{"className":20918,"style":644},[543],[61,20920,20922,20925,20968,20971,20974],{"className":20921},[114],[61,20923],{"className":20924,"style":18081},[118],[61,20926,20928],{"className":20927,"style":200},[123],[61,20929,20931,20934],{"className":20930},[123],[61,20932,58],{"className":20933,"style":333},[123,167],[61,20935,20937],{"className":20936},[8715],[61,20938,20940,20960],{"className":20939},[135,136],[61,20941,20943,20957],{"className":20942},[140],[61,20944,20946],{"className":20945,"style":18103},[144],[61,20947,20948,20951],{"style":19507},[61,20949],{"className":20950,"style":6445},[152],[61,20952,20954],{"className":20953},[157,158,159,160],[61,20955,18060],{"className":20956},[123,160],[61,20958,209],{"className":20959},[208],[61,20961,20963],{"className":20962},[140],[61,20964,20966],{"className":20965,"style":12205},[144],[61,20967],{},[61,20969],{"className":20970,"style":544},[543],[61,20972,444],{"className":20973},[548],[61,20975],{"className":20976,"style":544},[543],[61,20978,20980,20983,20989,20992,20995],{"className":20979},[114],[61,20981],{"className":20982,"style":407},[118],[61,20984,20986],{"className":20985,"style":200},[123],[61,20987,9078],{"className":20988,"style":9156},[123,167],[61,20990],{"className":20991,"style":644},[543],[61,20993,6856],{"className":20994},[648],[61,20996],{"className":20997,"style":644},[543],[61,20999,21001,21004],{"className":21000},[114],[61,21002],{"className":21003,"style":18081},[118],[61,21005,21007],{"className":21006,"style":200},[123],[61,21008,21010,21013],{"className":21009},[123],[61,21011,58],{"className":21012,"style":333},[123,167],[61,21014,21016],{"className":21015},[8715],[61,21017,21019,21039],{"className":21018},[135,136],[61,21020,21022,21036],{"className":21021},[140],[61,21023,21025],{"className":21024,"style":18103},[144],[61,21026,21027,21030],{"style":19507},[61,21028],{"className":21029,"style":6445},[152],[61,21031,21033],{"className":21032},[157,158,159,160],[61,21034,8427],{"className":21035},[123,160],[61,21037,209],{"className":21038},[208],[61,21040,21042],{"className":21041},[140],[61,21043,21045],{"className":21044,"style":12205},[144],[61,21046],{},[14,21048,21049],{},[228,21050,21053],{"href":21051,"rel":21052},"https:\u002F\u002Fimgse.com\u002Fi\u002FpF1n1sS",[9834],[9836,21054],{"alt":21055,"src":21056},"pF1n1sS.md.jpg","https:\u002F\u002Fs11.ax1x.com\u002F2024\u002F02\u002F06\u002FpF1n1sS.md.jpg",[14,21058,21059,21060,21256],{},"再图里面看是不是就很明显，",[61,21061,21063,21104],{"className":21062},[64],[61,21064,21066],{"className":21065},[68],[70,21067,21068],{"xmlns":72},[74,21069,21070,21102],{},[77,21071,21072,21076,21078,21086,21088,21092,21094],{},[89,21073,21074],{"style":91},[85,21075,9078],{},[442,21077,6856],{},[89,21079,21080],{"style":91},[12029,21081,21082,21084],{},[85,21083,58],{},[6846,21085,18060],{},[442,21087,444],{},[89,21089,21090],{"style":91},[85,21091,9078],{},[442,21093,6856],{},[89,21095,21096],{"style":91},[12029,21097,21098,21100],{},[85,21099,58],{},[6846,21101,8427],{},[102,21103,20894],{"encoding":104},[61,21105,21107,21128,21186,21207],{"className":21106,"ariaHidden":110},[109],[61,21108,21110,21113,21119,21122,21125],{"className":21109},[114],[61,21111],{"className":21112,"style":407},[118],[61,21114,21116],{"className":21115,"style":200},[123],[61,21117,9078],{"className":21118,"style":9156},[123,167],[61,21120],{"className":21121,"style":644},[543],[61,21123,6856],{"className":21124},[648],[61,21126],{"className":21127,"style":644},[543],[61,21129,21131,21134,21177,21180,21183],{"className":21130},[114],[61,21132],{"className":21133,"style":18081},[118],[61,21135,21137],{"className":21136,"style":200},[123],[61,21138,21140,21143],{"className":21139},[123],[61,21141,58],{"className":21142,"style":333},[123,167],[61,21144,21146],{"className":21145},[8715],[61,21147,21149,21169],{"className":21148},[135,136],[61,21150,21152,21166],{"className":21151},[140],[61,21153,21155],{"className":21154,"style":18103},[144],[61,21156,21157,21160],{"style":19507},[61,21158],{"className":21159,"style":6445},[152],[61,21161,21163],{"className":21162},[157,158,159,160],[61,21164,18060],{"className":21165},[123,160],[61,21167,209],{"className":21168},[208],[61,21170,21172],{"className":21171},[140],[61,21173,21175],{"className":21174,"style":12205},[144],[61,21176],{},[61,21178],{"className":21179,"style":544},[543],[61,21181,444],{"className":21182},[548],[61,21184],{"className":21185,"style":544},[543],[61,21187,21189,21192,21198,21201,21204],{"className":21188},[114],[61,21190],{"className":21191,"style":407},[118],[61,21193,21195],{"className":21194,"style":200},[123],[61,21196,9078],{"className":21197,"style":9156},[123,167],[61,21199],{"className":21200,"style":644},[543],[61,21202,6856],{"className":21203},[648],[61,21205],{"className":21206,"style":644},[543],[61,21208,21210,21213],{"className":21209},[114],[61,21211],{"className":21212,"style":18081},[118],[61,21214,21216],{"className":21215,"style":200},[123],[61,21217,21219,21222],{"className":21218},[123],[61,21220,58],{"className":21221,"style":333},[123,167],[61,21223,21225],{"className":21224},[8715],[61,21226,21228,21248],{"className":21227},[135,136],[61,21229,21231,21245],{"className":21230},[140],[61,21232,21234],{"className":21233,"style":18103},[144],[61,21235,21236,21239],{"style":19507},[61,21237],{"className":21238,"style":6445},[152],[61,21240,21242],{"className":21241},[157,158,159,160],[61,21243,8427],{"className":21244},[123,160],[61,21246,209],{"className":21247},[208],[61,21249,21251],{"className":21250},[140],[61,21252,21254],{"className":21253,"style":12205},[144],[61,21255],{},"意思就是沿杆的方向速度相等（图片中两个速度显然不符合实际情况）",[14,21258,21259],{},"————显然是废话{bushi}",[14,21261,21262],{},"从这里面其实我们就能更加深刻的理解，平时我们所说的沿杆的方向速度相等的更深层次的原理，而不是一些物理直觉（当然直觉也是有理有据的）",[14,21264,21265,21266,21436,21437,21471,21472,21505],{},"我们再看",[61,21267,21269,21305],{"className":21268},[64],[61,21270,21272],{"className":21271},[68],[70,21273,21274],{"xmlns":72},[74,21275,21276,21302],{},[77,21277,21278,21286,21288,21296,21298],{},[89,21279,21280],{"style":91},[12029,21281,21282,21284],{},[85,21283,52],{},[6846,21285,18060],{},[442,21287,6945],{},[89,21289,21290],{"style":91},[12029,21291,21292,21294],{},[85,21293,52],{},[6846,21295,8427],{},[442,21297,444],{},[89,21299,21300],{"style":91},[85,21301,9078],{},[102,21303,21304],{"encoding":104},"\\pmb{r_1}-\\pmb{r_2}=\\pmb{l}",[61,21306,21308,21366,21424],{"className":21307,"ariaHidden":110},[109],[61,21309,21311,21314,21357,21360,21363],{"className":21310},[114],[61,21312],{"className":21313,"style":20735},[118],[61,21315,21317],{"className":21316,"style":200},[123],[61,21318,21320,21323],{"className":21319},[123],[61,21321,52],{"className":21322,"style":204},[123,167],[61,21324,21326],{"className":21325},[8715],[61,21327,21329,21349],{"className":21328},[135,136],[61,21330,21332,21346],{"className":21331},[140],[61,21333,21335],{"className":21334,"style":18103},[144],[61,21336,21337,21340],{"style":18106},[61,21338],{"className":21339,"style":6445},[152],[61,21341,21343],{"className":21342},[157,158,159,160],[61,21344,18060],{"className":21345},[123,160],[61,21347,209],{"className":21348},[208],[61,21350,21352],{"className":21351},[140],[61,21353,21355],{"className":21354,"style":12205},[144],[61,21356],{},[61,21358],{"className":21359,"style":644},[543],[61,21361,6945],{"className":21362},[648],[61,21364],{"className":21365,"style":644},[543],[61,21367,21369,21372,21415,21418,21421],{"className":21368},[114],[61,21370],{"className":21371,"style":18081},[118],[61,21373,21375],{"className":21374,"style":200},[123],[61,21376,21378,21381],{"className":21377},[123],[61,21379,52],{"className":21380,"style":204},[123,167],[61,21382,21384],{"className":21383},[8715],[61,21385,21387,21407],{"className":21386},[135,136],[61,21388,21390,21404],{"className":21389},[140],[61,21391,21393],{"className":21392,"style":18103},[144],[61,21394,21395,21398],{"style":18106},[61,21396],{"className":21397,"style":6445},[152],[61,21399,21401],{"className":21400},[157,158,159,160],[61,21402,8427],{"className":21403},[123,160],[61,21405,209],{"className":21406},[208],[61,21408,21410],{"className":21409},[140],[61,21411,21413],{"className":21412,"style":12205},[144],[61,21414],{},[61,21416],{"className":21417,"style":544},[543],[61,21419,444],{"className":21420},[548],[61,21422],{"className":21423,"style":544},[543],[61,21425,21427,21430],{"className":21426},[114],[61,21428],{"className":21429,"style":407},[118],[61,21431,21433],{"className":21432,"style":200},[123],[61,21434,9078],{"className":21435,"style":9156},[123,167],"这个式子，在平面中，",[61,21438,21440,21456],{"className":21439},[64],[61,21441,21443],{"className":21442},[68],[70,21444,21445],{"xmlns":72},[74,21446,21447,21453],{},[77,21448,21449],{},[89,21450,21451],{"style":91},[85,21452,9078],{},[102,21454,21455],{"encoding":104},"\\pmb{l}",[61,21457,21459],{"className":21458,"ariaHidden":110},[109],[61,21460,21462,21465],{"className":21461},[114],[61,21463],{"className":21464,"style":407},[118],[61,21466,21468],{"className":21467,"style":200},[123],[61,21469,9078],{"className":21470,"style":9156},[123,167],"往往是以平动加转动的方式在“运动”，那么我们尝试对",[61,21473,21475,21490],{"className":21474},[64],[61,21476,21478],{"className":21477},[68],[70,21479,21480],{"xmlns":72},[74,21481,21482,21488],{},[77,21483,21484],{},[89,21485,21486],{"style":91},[85,21487,9078],{},[102,21489,21455],{"encoding":104},[61,21491,21493],{"className":21492,"ariaHidden":110},[109],[61,21494,21496,21499],{"className":21495},[114],[61,21497],{"className":21498,"style":407},[118],[61,21500,21502],{"className":21501,"style":200},[123],[61,21503,9078],{"className":21504,"style":9156},[123,167],"进行求导，",[14,21507,21508],{},"显然，这和上面旋转坐标系那里提及的求导方式是一致的，",[61,21510,21512],{"className":21511},[421],[61,21513,21515,21553],{"className":21514},[64],[61,21516,21518],{"className":21517},[68],[70,21519,21520],{"xmlns":72,"display":430},[74,21521,21522,21550],{},[77,21523,21524,21540,21542,21545,21547],{},[80,21525,21526,21534],{},[77,21527,21528,21530],{},[85,21529,87],{},[89,21531,21532],{"style":91},[85,21533,9078],{},[77,21535,21536,21538],{},[85,21537,87],{},[85,21539,100],{},[442,21541,444],{},[1817,21543,21544],{},"对长度的求导",[442,21546,472],{},[1817,21548,21549],{},"对方向的求导",[102,21551,21552],{"encoding":104},"\\frac{d\\pmb{l}}{dt}=对长度的求导+对方向的求导",[61,21554,21556,21642,21661],{"className":21555,"ariaHidden":110},[109],[61,21557,21559,21562,21633,21636,21639],{"className":21558},[114],[61,21560],{"className":21561,"style":558},[118],[61,21563,21565,21568,21630],{"className":21564},[123],[61,21566],{"className":21567},[127,128],[61,21569,21571],{"className":21570},[80],[61,21572,21574,21622],{"className":21573},[135,136],[61,21575,21577,21619],{"className":21576},[140],[61,21578,21580,21594,21602],{"className":21579,"style":577},[144],[61,21581,21582,21585],{"style":580},[61,21583],{"className":21584,"style":153},[152],[61,21586,21588,21591],{"className":21587},[123],[61,21589,87],{"className":21590},[123,167],[61,21592,100],{"className":21593},[123,167],[61,21595,21596,21599],{"style":173},[61,21597],{"className":21598,"style":153},[152],[61,21600],{"className":21601,"style":181},[180],[61,21603,21604,21607],{"style":604},[61,21605],{"className":21606,"style":153},[152],[61,21608,21610,21613],{"className":21609},[123],[61,21611,87],{"className":21612},[123,167],[61,21614,21616],{"className":21615,"style":200},[123],[61,21617,9078],{"className":21618,"style":9156},[123,167],[61,21620,209],{"className":21621},[208],[61,21623,21625],{"className":21624},[140],[61,21626,21628],{"className":21627,"style":629},[144],[61,21629],{},[61,21631],{"className":21632},[222,128],[61,21634],{"className":21635,"style":544},[543],[61,21637,444],{"className":21638},[548],[61,21640],{"className":21641,"style":544},[543],[61,21643,21645,21649,21652,21655,21658],{"className":21644},[114],[61,21646],{"className":21647,"style":21648},[118],"height:0.7667em;vertical-align:-0.0833em;",[61,21650,21544],{"className":21651},[123,1885],[61,21653],{"className":21654,"style":644},[543],[61,21656,472],{"className":21657},[648],[61,21659],{"className":21660,"style":644},[543],[61,21662,21664,21667],{"className":21663},[114],[61,21665],{"className":21666,"style":10040},[118],[61,21668,21549],{"className":21669},[123,1885],[61,21671,21673],{"className":21672},[421],[61,21674,21676,21706],{"className":21675},[64],[61,21677,21679],{"className":21678},[68],[70,21680,21681],{"xmlns":72,"display":430},[74,21682,21683,21703],{},[77,21684,21685,21687,21691,21693,21697,21699],{},[442,21686,444],{},[89,21688,21689],{"style":91},[6846,21690,447],{},[442,21692,472],{},[89,21694,21695],{"style":91},[85,21696,11900],{},[442,21698,12073],{},[89,21700,21701],{"style":91},[85,21702,9078],{},[102,21704,21705],{"encoding":104},"=\\pmb{0}+\\pmb{\\omega}\\times\\pmb{l}",[61,21707,21709,21721,21742,21763],{"className":21708,"ariaHidden":110},[109],[61,21710,21712,21715,21718],{"className":21711},[114],[61,21713],{"className":21714,"style":2726},[118],[61,21716,444],{"className":21717},[548],[61,21719],{"className":21720,"style":544},[543],[61,21722,21724,21727,21733,21736,21739],{"className":21723},[114],[61,21725],{"className":21726,"style":7318},[118],[61,21728,21730],{"className":21729,"style":200},[123],[61,21731,447],{"className":21732},[123],[61,21734],{"className":21735,"style":644},[543],[61,21737,472],{"className":21738},[648],[61,21740],{"className":21741,"style":644},[543],[61,21743,21745,21748,21754,21757,21760],{"className":21744},[114],[61,21746],{"className":21747,"style":10438},[118],[61,21749,21751],{"className":21750,"style":200},[123],[61,21752,11900],{"className":21753,"style":333},[123,167],[61,21755],{"className":21756,"style":644},[543],[61,21758,12073],{"className":21759},[648],[61,21761],{"className":21762,"style":644},[543],[61,21764,21766,21769],{"className":21765},[114],[61,21767],{"className":21768,"style":407},[118],[61,21770,21772],{"className":21771,"style":200},[123],[61,21773,9078],{"className":21774,"style":9156},[123,167],[61,21776,21778],{"className":21777},[421],[61,21779,21781,21805],{"className":21780},[64],[61,21782,21784],{"className":21783},[68],[70,21785,21786],{"xmlns":72,"display":430},[74,21787,21788,21802],{},[77,21789,21790,21792,21796,21798],{},[442,21791,444],{},[89,21793,21794],{"style":91},[85,21795,11900],{},[442,21797,12073],{},[89,21799,21800],{"style":91},[85,21801,9078],{},[102,21803,21804],{"encoding":104},"=\\pmb{\\omega}\\times\\pmb{l}",[61,21806,21808,21820,21841],{"className":21807,"ariaHidden":110},[109],[61,21809,21811,21814,21817],{"className":21810},[114],[61,21812],{"className":21813,"style":2726},[118],[61,21815,444],{"className":21816},[548],[61,21818],{"className":21819,"style":544},[543],[61,21821,21823,21826,21832,21835,21838],{"className":21822},[114],[61,21824],{"className":21825,"style":10438},[118],[61,21827,21829],{"className":21828,"style":200},[123],[61,21830,11900],{"className":21831,"style":333},[123,167],[61,21833],{"className":21834,"style":644},[543],[61,21836,12073],{"className":21837},[648],[61,21839],{"className":21840,"style":644},[543],[61,21842,21844,21847],{"className":21843},[114],[61,21845],{"className":21846,"style":407},[118],[61,21848,21850],{"className":21849,"style":200},[123],[61,21851,9078],{"className":21852,"style":9156},[123,167],[61,21854,21856],{"className":21855},[421],[61,21857,21859,21901],{"className":21858},[64],[61,21860,21862],{"className":21861},[68],[70,21863,21864],{"xmlns":72,"display":430},[74,21865,21866,21898],{},[77,21867,21868,21871,21879,21881,21889,21891,21895],{},[1817,21869,21870],{},"也就是说对",[89,21872,21873],{"style":91},[12029,21874,21875,21877],{},[85,21876,52],{},[6846,21878,18060],{},[442,21880,6945],{},[89,21882,21883],{"style":91},[12029,21884,21885,21887],{},[85,21886,52],{},[6846,21888,8427],{},[442,21890,444],{},[89,21892,21893],{"style":91},[85,21894,9078],{},[1817,21896,21897],{},"两边求导，会得到——",[102,21899,21900],{"encoding":104},"也就是说对\\pmb{r_1}-\\pmb{r_2}=\\pmb{l}两边求导，会得到——",[61,21902,21904,21966,22024],{"className":21903,"ariaHidden":110},[109],[61,21905,21907,21911,21914,21957,21960,21963],{"className":21906},[114],[61,21908],{"className":21909,"style":21910},[118],"height:0.8333em;vertical-align:-0.15em;",[61,21912,21870],{"className":21913},[123,1885],[61,21915,21917],{"className":21916,"style":200},[123],[61,21918,21920,21923],{"className":21919},[123],[61,21921,52],{"className":21922,"style":204},[123,167],[61,21924,21926],{"className":21925},[8715],[61,21927,21929,21949],{"className":21928},[135,136],[61,21930,21932,21946],{"className":21931},[140],[61,21933,21935],{"className":21934,"style":18103},[144],[61,21936,21937,21940],{"style":18106},[61,21938],{"className":21939,"style":6445},[152],[61,21941,21943],{"className":21942},[157,158,159,160],[61,21944,18060],{"className":21945},[123,160],[61,21947,209],{"className":21948},[208],[61,21950,21952],{"className":21951},[140],[61,21953,21955],{"className":21954,"style":12205},[144],[61,21956],{},[61,21958],{"className":21959,"style":644},[543],[61,21961,6945],{"className":21962},[648],[61,21964],{"className":21965,"style":644},[543],[61,21967,21969,21972,22015,22018,22021],{"className":21968},[114],[61,21970],{"className":21971,"style":18081},[118],[61,21973,21975],{"className":21974,"style":200},[123],[61,21976,21978,21981],{"className":21977},[123],[61,21979,52],{"className":21980,"style":204},[123,167],[61,21982,21984],{"className":21983},[8715],[61,21985,21987,22007],{"className":21986},[135,136],[61,21988,21990,22004],{"className":21989},[140],[61,21991,21993],{"className":21992,"style":18103},[144],[61,21994,21995,21998],{"style":18106},[61,21996],{"className":21997,"style":6445},[152],[61,21999,22001],{"className":22000},[157,158,159,160],[61,22002,8427],{"className":22003},[123,160],[61,22005,209],{"className":22006},[208],[61,22008,22010],{"className":22009},[140],[61,22011,22013],{"className":22012,"style":12205},[144],[61,22014],{},[61,22016],{"className":22017,"style":544},[543],[61,22019,444],{"className":22020},[548],[61,22022],{"className":22023,"style":544},[543],[61,22025,22027,22030,22036,22040],{"className":22026},[114],[61,22028],{"className":22029,"style":407},[118],[61,22031,22033],{"className":22032,"style":200},[123],[61,22034,9078],{"className":22035,"style":9156},[123,167],[61,22037,22039],{"className":22038},[123,1885],"两边求导，会得到",[61,22041,22043],{"className":22042},[123],"——",[61,22045,22047],{"className":22046},[421],[61,22048,22050,22092],{"className":22049},[64],[61,22051,22053],{"className":22052},[68],[70,22054,22055],{"xmlns":72,"display":430},[74,22056,22057,22089],{},[77,22058,22059,22067,22069,22077,22079,22083,22085],{},[89,22060,22061],{"style":91},[12029,22062,22063,22065],{},[85,22064,58],{},[6846,22066,18060],{},[442,22068,6945],{},[89,22070,22071],{"style":91},[12029,22072,22073,22075],{},[85,22074,58],{},[6846,22076,8427],{},[442,22078,444],{},[89,22080,22081],{"style":91},[85,22082,11900],{},[442,22084,12073],{},[89,22086,22087],{"style":91},[85,22088,9078],{},[102,22090,22091],{"encoding":104},"\\pmb{v_1}-\\pmb{v_2}=\\pmb{\\omega}\\times\\pmb{l}",[61,22093,22095,22153,22211,22232],{"className":22094,"ariaHidden":110},[109],[61,22096,22098,22101,22144,22147,22150],{"className":22097},[114],[61,22099],{"className":22100,"style":20735},[118],[61,22102,22104],{"className":22103,"style":200},[123],[61,22105,22107,22110],{"className":22106},[123],[61,22108,58],{"className":22109,"style":333},[123,167],[61,22111,22113],{"className":22112},[8715],[61,22114,22116,22136],{"className":22115},[135,136],[61,22117,22119,22133],{"className":22118},[140],[61,22120,22122],{"className":22121,"style":18103},[144],[61,22123,22124,22127],{"style":19507},[61,22125],{"className":22126,"style":6445},[152],[61,22128,22130],{"className":22129},[157,158,159,160],[61,22131,18060],{"className":22132},[123,160],[61,22134,209],{"className":22135},[208],[61,22137,22139],{"className":22138},[140],[61,22140,22142],{"className":22141,"style":12205},[144],[61,22143],{},[61,22145],{"className":22146,"style":644},[543],[61,22148,6945],{"className":22149},[648],[61,22151],{"className":22152,"style":644},[543],[61,22154,22156,22159,22202,22205,22208],{"className":22155},[114],[61,22157],{"className":22158,"style":18081},[118],[61,22160,22162],{"className":22161,"style":200},[123],[61,22163,22165,22168],{"className":22164},[123],[61,22166,58],{"className":22167,"style":333},[123,167],[61,22169,22171],{"className":22170},[8715],[61,22172,22174,22194],{"className":22173},[135,136],[61,22175,22177,22191],{"className":22176},[140],[61,22178,22180],{"className":22179,"style":18103},[144],[61,22181,22182,22185],{"style":19507},[61,22183],{"className":22184,"style":6445},[152],[61,22186,22188],{"className":22187},[157,158,159,160],[61,22189,8427],{"className":22190},[123,160],[61,22192,209],{"className":22193},[208],[61,22195,22197],{"className":22196},[140],[61,22198,22200],{"className":22199,"style":12205},[144],[61,22201],{},[61,22203],{"className":22204,"style":544},[543],[61,22206,444],{"className":22207},[548],[61,22209],{"className":22210,"style":544},[543],[61,22212,22214,22217,22223,22226,22229],{"className":22213},[114],[61,22215],{"className":22216,"style":10438},[118],[61,22218,22220],{"className":22219,"style":200},[123],[61,22221,11900],{"className":22222,"style":333},[123,167],[61,22224],{"className":22225,"style":644},[543],[61,22227,12073],{"className":22228},[648],[61,22230],{"className":22231,"style":644},[543],[61,22233,22235,22238],{"className":22234},[114],[61,22236],{"className":22237,"style":407},[118],[61,22239,22241],{"className":22240,"style":200},[123],[61,22242,9078],{"className":22243,"style":9156},[123,167],[14,22245,22246],{},"这个式子我们再看，它有用了起来",[14,22248,22249,22445],{},[61,22250,22252,22293],{"className":22251},[64],[61,22253,22255],{"className":22254},[68],[70,22256,22257],{"xmlns":72},[74,22258,22259,22291],{},[77,22260,22261,22269,22271,22279,22281,22285,22287],{},[89,22262,22263],{"style":91},[12029,22264,22265,22267],{},[85,22266,58],{},[6846,22268,18060],{},[442,22270,6945],{},[89,22272,22273],{"style":91},[12029,22274,22275,22277],{},[85,22276,58],{},[6846,22278,8427],{},[442,22280,444],{},[89,22282,22283],{"style":91},[85,22284,11900],{},[442,22286,12073],{},[89,22288,22289],{"style":91},[85,22290,9078],{},[102,22292,22091],{"encoding":104},[61,22294,22296,22354,22412,22433],{"className":22295,"ariaHidden":110},[109],[61,22297,22299,22302,22345,22348,22351],{"className":22298},[114],[61,22300],{"className":22301,"style":20735},[118],[61,22303,22305],{"className":22304,"style":200},[123],[61,22306,22308,22311],{"className":22307},[123],[61,22309,58],{"className":22310,"style":333},[123,167],[61,22312,22314],{"className":22313},[8715],[61,22315,22317,22337],{"className":22316},[135,136],[61,22318,22320,22334],{"className":22319},[140],[61,22321,22323],{"className":22322,"style":18103},[144],[61,22324,22325,22328],{"style":19507},[61,22326],{"className":22327,"style":6445},[152],[61,22329,22331],{"className":22330},[157,158,159,160],[61,22332,18060],{"className":22333},[123,160],[61,22335,209],{"className":22336},[208],[61,22338,22340],{"className":22339},[140],[61,22341,22343],{"className":22342,"style":12205},[144],[61,22344],{},[61,22346],{"className":22347,"style":644},[543],[61,22349,6945],{"className":22350},[648],[61,22352],{"className":22353,"style":644},[543],[61,22355,22357,22360,22403,22406,22409],{"className":22356},[114],[61,22358],{"className":22359,"style":18081},[118],[61,22361,22363],{"className":22362,"style":200},[123],[61,22364,22366,22369],{"className":22365},[123],[61,22367,58],{"className":22368,"style":333},[123,167],[61,22370,22372],{"className":22371},[8715],[61,22373,22375,22395],{"className":22374},[135,136],[61,22376,22378,22392],{"className":22377},[140],[61,22379,22381],{"className":22380,"style":18103},[144],[61,22382,22383,22386],{"style":19507},[61,22384],{"className":22385,"style":6445},[152],[61,22387,22389],{"className":22388},[157,158,159,160],[61,22390,8427],{"className":22391},[123,160],[61,22393,209],{"className":22394},[208],[61,22396,22398],{"className":22397},[140],[61,22399,22401],{"className":22400,"style":12205},[144],[61,22402],{},[61,22404],{"className":22405,"style":544},[543],[61,22407,444],{"className":22408},[548],[61,22410],{"className":22411,"style":544},[543],[61,22413,22415,22418,22424,22427,22430],{"className":22414},[114],[61,22416],{"className":22417,"style":10438},[118],[61,22419,22421],{"className":22420,"style":200},[123],[61,22422,11900],{"className":22423,"style":333},[123,167],[61,22425],{"className":22426,"style":644},[543],[61,22428,12073],{"className":22429},[648],[61,22431],{"className":22432,"style":644},[543],[61,22434,22436,22439],{"className":22435},[114],[61,22437],{"className":22438,"style":407},[118],[61,22440,22442],{"className":22441,"style":200},[123],[61,22443,9078],{"className":22444,"style":9156},[123,167],"  其实就是以一个端点为参考系，另一个端点必然是绕原来的端点（在系中静止的）圆周运动",[14,22447,22448],{},"再求导可以得到",[61,22450,22452],{"className":22451},[421],[61,22453,22455,22587],{"className":22454},[64],[61,22456,22458],{"className":22457},[68],[70,22459,22460],{"xmlns":72,"display":430},[74,22461,22462,22584],{},[77,22463,22464,22472,22474,22482,22484,22510,22512,22514,22518,22520,22524,22526,22530,22532,22548,22550,22552,22556,22558,22562,22564,22568,22570,22572,22576,22578,22582],{},[89,22465,22466],{"style":91},[12029,22467,22468,22470],{},[85,22469,228],{},[6846,22471,18060],{},[442,22473,6945],{},[89,22475,22476],{"style":91},[12029,22477,22478,22480],{},[85,22479,228],{},[6846,22481,8427],{},[442,22483,444],{},[80,22485,22486,22504],{},[77,22487,22488,22490,22492,22496,22498,22502],{},[85,22489,87],{},[442,22491,6942],{"stretchy":6941},[89,22493,22494],{"style":91},[85,22495,11900],{},[442,22497,12073],{},[89,22499,22500],{"style":91},[85,22501,9078],{},[442,22503,6956],{"stretchy":6941},[77,22505,22506,22508],{},[85,22507,87],{},[85,22509,100],{},[543,22511],{"linebreak":6842},[442,22513,444],{},[89,22515,22516],{"style":91},[85,22517,14586],{},[442,22519,12073],{},[89,22521,22522],{"style":91},[85,22523,9078],{},[442,22525,472],{},[89,22527,22528],{"style":91},[85,22529,11900],{},[442,22531,12073],{},[80,22533,22534,22542],{},[77,22535,22536,22538],{},[85,22537,87],{},[89,22539,22540],{"style":91},[85,22541,9078],{},[77,22543,22544,22546],{},[85,22545,87],{},[85,22547,100],{},[543,22549],{"linebreak":6842},[442,22551,444],{},[89,22553,22554],{"style":91},[85,22555,14586],{},[442,22557,12073],{},[89,22559,22560],{"style":91},[85,22561,9078],{},[442,22563,472],{},[89,22565,22566],{"style":91},[85,22567,11900],{},[442,22569,12073],{},[442,22571,6942],{"stretchy":6941},[89,22573,22574],{"style":91},[85,22575,11900],{},[442,22577,12073],{},[89,22579,22580],{"style":91},[85,22581,9078],{},[442,22583,6956],{"stretchy":6941},[102,22585,22586],{"encoding":104},"\\pmb{a_1}-\\pmb{a_2}=\\frac{d(\\pmb{\\omega}\\times\\pmb{l})}{dt}\\\\\n=\\pmb{\\beta}\\times\\pmb{l}+\\pmb{\\omega}\\times\\frac{d\\pmb{l}}{dt}\\\\\n=\\pmb{\\beta}\\times\\pmb{l}+\\pmb{\\omega}\\times(\\pmb{\\omega}\\times\\pmb{l})",[61,22588,22590,22648,22706,22804,22807,22819,22840,22861,22882,22959,22962,22974,22995,23016,23037,23061],{"className":22589,"ariaHidden":110},[109],[61,22591,22593,22596,22639,22642,22645],{"className":22592},[114],[61,22594],{"className":22595,"style":20735},[118],[61,22597,22599],{"className":22598,"style":200},[123],[61,22600,22602,22605],{"className":22601},[123],[61,22603,228],{"className":22604},[123,167],[61,22606,22608],{"className":22607},[8715],[61,22609,22611,22631],{"className":22610},[135,136],[61,22612,22614,22628],{"className":22613},[140],[61,22615,22617],{"className":22616,"style":18103},[144],[61,22618,22619,22622],{"style":12185},[61,22620],{"className":22621,"style":6445},[152],[61,22623,22625],{"className":22624},[157,158,159,160],[61,22626,18060],{"className":22627},[123,160],[61,22629,209],{"className":22630},[208],[61,22632,22634],{"className":22633},[140],[61,22635,22637],{"className":22636,"style":12205},[144],[61,22638],{},[61,22640],{"className":22641,"style":644},[543],[61,22643,6945],{"className":22644},[648],[61,22646],{"className":22647,"style":644},[543],[61,22649,22651,22654,22697,22700,22703],{"className":22650},[114],[61,22652],{"className":22653,"style":18081},[118],[61,22655,22657],{"className":22656,"style":200},[123],[61,22658,22660,22663],{"className":22659},[123],[61,22661,228],{"className":22662},[123,167],[61,22664,22666],{"className":22665},[8715],[61,22667,22669,22689],{"className":22668},[135,136],[61,22670,22672,22686],{"className":22671},[140],[61,22673,22675],{"className":22674,"style":18103},[144],[61,22676,22677,22680],{"style":12185},[61,22678],{"className":22679,"style":6445},[152],[61,22681,22683],{"className":22682},[157,158,159,160],[61,22684,8427],{"className":22685},[123,160],[61,22687,209],{"className":22688},[208],[61,22690,22692],{"className":22691},[140],[61,22693,22695],{"className":22694,"style":12205},[144],[61,22696],{},[61,22698],{"className":22699,"style":544},[543],[61,22701,444],{"className":22702},[548],[61,22704],{"className":22705,"style":544},[543],[61,22707,22709,22712],{"className":22708},[114],[61,22710],{"className":22711,"style":13565},[118],[61,22713,22715,22718,22801],{"className":22714},[123],[61,22716],{"className":22717},[127,128],[61,22719,22721],{"className":22720},[80],[61,22722,22724,22793],{"className":22723},[135,136],[61,22725,22727,22790],{"className":22726},[140],[61,22728,22730,22744,22752],{"className":22729,"style":13587},[144],[61,22731,22732,22735],{"style":580},[61,22733],{"className":22734,"style":153},[152],[61,22736,22738,22741],{"className":22737},[123],[61,22739,87],{"className":22740},[123,167],[61,22742,100],{"className":22743},[123,167],[61,22745,22746,22749],{"style":173},[61,22747],{"className":22748,"style":153},[152],[61,22750],{"className":22751,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