动力学普遍方程及拉格朗日方程概要课件.ppt

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,2122IIsinmlFFBA0211IICBABBAAygmygmygmxFxFcos2cossincossinlylylxlylxCBBAAsin2si

2、ncossincoslylylxlylxCBBAA0211IICBABBAAygmygmygmxFxFsin2sincossincoslylylxlylxCBBAA0sin2sin2cossin22121glmglmllmcos)(1212lmgmm 11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ00，x00，x0cossin22r2Ie2I2JRFRFRgm0)23cos(1sinr1aag00，x11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa cos)(2121mammar00，x0cos)(r2Ie2I1IxFxFF11

3、I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa 222121r222121cos2)3()(sin2cos2)3(sin2mmmmmgammmgmacos)(2121mammar0)23cos(1sinr1aag12,NF FF12,Nrrr12,nq qq12(,)iinq qq trr110NNiiiiiiimFrar11NniijjijQqFrjQ1niijjjqqrr1Niiiimar1111()0NNnNiiiiiiji ijiijijmQmqqrFrarr10(1,2,)Niji iijQmjnqrr1111()NnnNiii iji ijijji

4、jjrrmqmqqq rr111()()Nii iijNNiiiii iiijjmqddmmdtqdtqrrrrrriijjqqrr函数，函数，仅为时间和广义坐标的仅为时间和广义坐标的和和jiiqtrr无无关关与与广广义义速速度度jq 1ddnjiiijjjjqqqtqtrrr广广义义速速度度1niiikkkqtqrrr221niiikkjjjkqqqtqqrrrkNkkjijijiqqqtqqt122ddrrrijq rddijtqr111()()NNNiiii iiii iiiijjjddmmmqdtqdtqrrrrrr1111()NNiiiii iiijjNNiiii iiijjdmmd

5、tqqdmmdtqqrrrrrrrr2111111()()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,)jnOARr2222212121AAAOJvmJT2221)(92(

6、121rRmmrrRrvrRvAAA)(OARr2222212121AAAOJvmJT2221)(92(121rRmmMMWQFQTTt)(ddMrRmm 221)(92(61221)(92(6rRmmM 002221)(92(3ttrRmmMCROxx22221212121CCJvmxmT2221RmJRxvCC222222143)(21RmxRmxmmgfmmFxxFFxWQsFx)()(2100，x00，x0FWQxQxTxTt)(dd RmxmmxTdtdRmxmmxT221221)()(gfmmFRmxmm)()(21221 QTTt)(dd 2222222323RmxRmxTRmx

7、RmT023222 RmxRm3)(2121mmgmmfFa解得：解得：222222143)(21RmxRmxmmT0QgfmmFQx)(21222121CCJmvTcos2sin2lylyCCsin2cos2lxxlxxCC)31sin(2121)cos21()sin2(21222222llxxmJlxmTC)cos2(212lxmgkxV)cos2(212lxmgkxVTL)31sin(21222llxxm2121,2,1,qxqqxqkqk广义坐标广义坐标0)(ddkkqLqLtmgxkxxLsin21lmxmxLcos21sin21)(dd2lmlmxmxLt )cos2(212lxm

8、gkx)31sin(21222llxxmVTL0)(ddxLxLt0cos21sin212mgkxmlmlxm 0)(ddLLtcos21sin213)(dd2lxmxmlmlLt sin21cos21mgllxmLsin21312xmlmlL0sin21sin213gxl 0cos21sin212mgkxmlmlxm )cos2(212lxmgkx)31sin(21222llxxmVTLOACkxxyOACkxxy22222121212121CCOOJvmJxmTsin2cos2lylyCCcos2sin2lxxlxxCCcos212122glmkxVcos2161)23(412222221

9、x lmlmxmmTOACkxxy0)(ddkkqLqLtVTLcos2161)23(412222221x lmlmxmmcos212122glmkx2121,2,1,qxqqxqkqk广义坐标广义坐标kxxLcos21)23(21221lmxmmxLsin21cos21)23(21)(dd22221 lmlmxmmxLt0)(ddxLxLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos)23(22221kxlmlmxmm sin21sin2122glmxmLcos2131222x lmlmLsin21cos2131)(dd2222

10、x lmx lmlmxLt0)(ddLLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos32gxl 0sincos)23(22221kxlmlmxmm 222222112121212121OOOOOOJmvJmvT11,3OORv232,3222RvvRvRvrOErOrOErcos1249cos22222221222122RRRvvvvvrOOrOOO222222112121212121OOOOOOJmvJmvT11,3OORv2322RvvrOErOcos1249cos22222221222122RRRvvvvvrOOrOOO)c

11、os1(641822222mRmRmRcos2mgRV0)(ddkkqLqLtVTL2121,2,1,qqqqkqk广义坐标广义坐标)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 广广义义动动量量jjjjpconstpqTqLEVT)cos1(641822222mRmRmRTcos2mgRVcos2)cos1(641822222mgRmRmRmRVTLconstgRcos2)cos1(3922constLL,0const)cos1(6constgRcos2)cos1(3922const)cos1(60sin)cos1(34Rg 0sin)cos1(62 )21(0)(nimiiiii,raF ),2,1()(NkQqTqTdtdkkk),2,1(0)(NkqLqLdtdkk广广义义动动量量jjjjpconstpqTqLEVT