動力學(xué)普遍方程及拉格朗日方程ppt課件

1、R0(1,2,)iiiimiNFFa(1,2, , )iiNrR() 0(1,2,)iiiiiimiNFFarR0(1,2,)iiiiNFr()0(1,2,)iiiiimiNFarR() 0(1,2,)iiiiiimiNFFar() () () 01,2,ixiiiiyiiiiziiiiFm xxFm yyFm zziN()0(1,2,)iiiiimiNFarCmgaCCmaFIRCICJM0sinRxMxF-xmgICIRsin32gaCRamRJCC,2122IIsinmlFFBA0211IICBABBAAygmygmygmxFxFcos2cossincossinlylylxlylxCBB

2、AAsin2sincossincoslylylxlylxCBBAA0211IICBABBAAygmygmygmxFxFsin2sincossincoslylylxlylxCBBAA0sin2sin2cossin22121glmglmllmcos)(1212lmgmm 11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ00，x00，x0cossin22r2Ie2I2JRFRFRgm0)23cos(1sinr1aag00，x11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa cos)(2121mammar00，x0cos)(r2Ie2I1

3、IxFxFF11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa 222121r222121cos2)3()(sin2cos2)3(sin2mmmmmgammmgmacos)(2121mammar0)23cos(1sinr1aag12,NF FF12,Nrrr12,nq qq12( , )iinq qq trr110NNiiiiiiimFrar11NniijjijQqFrjQ1niijjjqqrr1Niiiimar1111()0NNnNiiiiiiji ijiijijmQmqqrFrarr10(1,2, )Niji iijQmjnqrr1111()NnnNiii

4、 iji ijijjijjrrmqmqqq rr111()()Nii iijNNiiiii iiijjmqddmmdtqdtqrrrrrriijjqqrr函數(shù)，函數(shù)，僅為時間和廣義坐標(biāo)的僅為時間和廣義坐標(biāo)的和和jiiqtrr無無關(guān)關(guān)與與廣廣義義速速度度jq 1ddnjiiijjjjqqqtqtrrr廣廣義義速速度度1niiikkkqtqrrr221niiikkjjjkqqqtqqrrrkNkkjijijiqqqtqqt122ddrrrijq rddijtqr111()()NNNiiii iiii iiiijjjddmmmqdtqdtqrrrrrr1111()NNiiiii iiijjNNiii

5、i iiijjdmmdtqqdmmdtqqrrrrrrrr2111111()()22NNNiii iiiiiiijjjjNiiijjTmmmvqqqqTmqq rrr rrr1Nii iijjjdTTmqdtqqrriijjqqrriijjddtqqrr10(1,2, )Niji iijQmjnqrr1Nii iijjjdTTmqdtqqrr(1,2, )jjjdTTQjndtqqjjVQq d()djjjTTVtqqq 12( , )0,(j1,2, )njVVV q qq tnqd()()0djjjjTVTVtqqqqd()0djjLLtqq(1,2, )jnOARr2222212121A

6、AAOJvmJT2221)(92(121rRmmrrRrvrRvAAA)(OARr2222212121AAAOJvmJT2221)(92(121rRmmMMWQFQTTt)(ddMrRmm 221)(92(61221)(92(6rRmmM 002221)(92(3ttrRmmMCROxx22221212121CCJvmxmT2221RmJRxvCC222222143)(21RmxRmxmmgfmmFxxFFxWQsFx)()(2100，x00，x0FWQxQxTxTt)(dd RmxmmxTdtdRmxmmxT221221)()(gfmmFRmxmm)()(21221 QTTt)(dd 222

7、2222323RmxRmxTRmxRmT023222 RmxRm3)(2121mmgmmfFa解得：解得：222222143)(21RmxRmxmmT0QgfmmFQx)(21222121CCJmvTcos2sin2lylyCCsin2cos2lxxlxxCC)31sin(2121)cos21()sin2(21222222llxxmJlxmTC)cos2(212lxmgkxV)cos2(212lxmgkxVTL)31sin(21222llxxm2121,2 , 1,qxqqxqkqk廣廣義義坐坐標(biāo)標(biāo)0)(ddkkqLqLtmgxkxxLsin21lmxmxLcos21sin21)(dd2lml

8、mxmxLt )cos2(212lxmgkx)31sin(21222llxxmVTL0)(ddxLxLt0cos21sin212mgkxmlmlxm 0)(ddLLtcos21sin213)(dd2lxmxmlmlLt sin21cos21mgllxmLsin21312xmlmlL0sin21sin213gxl 0cos21sin212mgkxmlmlxm )cos2(212lxmgkx)31sin(21222llxxmVTLOACkxxyOACkxxy22222121212121CCOOJvmJxmTsin2cos2lylyCCcos2sin2lxxlxxCCcos212122glmkxVc

9、os2161)23(412222221x lmlmxmmTOACkxxy0)(ddkkqLqLtVTLcos2161)23(412222221x lmlmxmmcos212122glmkx2121,2 , 1,qxqqxqkqk廣廣義義坐坐標(biāo)標(biāo)kxxLcos21)23(21221lmxmmxLsin21cos21)23(21)(dd22221 lmlmxmmxLt0)(ddxLxLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos)23(22221kxlmlmxmm sin21sin2122glmxmLcos2131222x lmlmL

10、sin21cos2131)(dd2222 x lmx lmlmxLt0)(ddLLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos32gxl 0sincos)23(22221kxlmlmxmm 222222112121212121OOOOOOJmvJmvT11,3OORv232,3222RvvRvRvrOErOrOErcos1249cos22222221222122RRRvvvvvrOOrOOO222222112121212121OOOOOOJmvJmvT11,3OORv2322RvvrOErOcos1249cos2222222122

11、2122RRRvvvvvrOOrOOO)cos1 (641822222mRmRmRcos2mgRV0)(ddkkqLqLtVTL2121,2 , 1,qqqqkqk廣廣義義坐坐標(biāo)標(biāo))cos1 (641822222mRmRmRcos2mgR0L)cos1(63622mRmRLsin6)cos1 (636)(dd2222 mRmRmRLt0)(ddLLt0sin)cos1 (62 cos2)cos1 (641822222mgRmRmRmRVTLsin2sin62mgRmRL)cos1(6822mRmRLsin6)cos1 (68)(dd222 mRmRmRLt0)(ddLLt0sin)cos1 (34Rg cos2)cos1 (641822222mgRmRmRmRVTL0sin)cos1 (62 廣廣義義動動量量jjjjpconstpqTqLEVT)cos1 (641822222mRmRmRTcos2mgRVcos2)cos1 (641822222mgRmRmRmRVTLconstgRcos2)cos1 (