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123),2,1(0Nnimiiii aFF),2,1(nii r),2,1(0)(Nnimiiiiii raFF4),2,1(0Nniiii rF),2,1(0)(nimiiiii raF),2,1(0)(Nnimiiiiii raFF5nizzmFyymFxxmFiiiziiiiyiiiiixi,2,10)()()(),2,1(0)(nimiiiii raF67CmgaCCmaFIRCICJM0sinRxMxF-xmgICIRsin32gaCRamRJCC,21282IIsinmlFFBA90211IICBABBAAygmygmygmxFxFcos2cossincossinlylylxlylxCBBAAsin2sincossincoslylylxlylxCBBAA100211IICBABBAAygmygmygmxFxFsin2sincossincoslylylxlylxCBBAA0sin2sin2cossin22121glmglmllmcos)(1212lmgmm 111211I1amF 12I2eamFr2I2ramF22I2JM22221RmJ00，x00，x130cossin22r2Ie2I2JRFRFRgm0)23cos(1sinr1aag00，x11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa 14cos)(2121mammar00，x0cos)(r2Ie2I1IxFxFF11I1amF 12I2eamFr2I2ramF22I2JM22221RmJ2rRa 15222121r222121cos2)3()(sin2cos2)3(sin2mmmmmgammmgmacos)(2121mammar0)23cos(1sinr1aag16),(21nFFFF ),(21nrrrr)(21Nqqqq,),(21tqqqNii rr011iniiiiniimrarFNkkkiniiqQ11rF17Nkkkiiqq1rriniiimra 10)(1111kkiniiiNkkiniiiiniiqqmQmrrrarF),2,1(01NkqmQnikiiik rrkkiniiiNkkNkkiniiiqqrmqqrm)(1111rr 18)()(111kiniiikiiniinikiiiqdtdmqdtdmqmrrrrrr(消消点点)第第一一个个拉拉格格朗朗日日关关系系式式kikiqqrr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 广义速度广义速度tqqqqtkkkNkkiiidd1rrr19kNkkiiiqqt1rrrkNkkjijijiqqqtqq122rrrkNkkjijijiqqqtqqt122ddrrrkiqr kiqtrdd20nikiiininikiiikiiiqdtdmqdtdmqm111)()(rrrrrr nikiiinikiinikiiinikiiiqmqmdtdqmqdtdm1111)(rrrrrrrrknikiikniiikniiiiknikiiqTqmqTvmqmqqm11211)(21)(21rrrrrrkknikiiiqTqTdtdqm 1rrkikiqqrrkikiqqdtdrr21),2,1(01NkqmQnikiiik rrkknikiiiqTqTdtdqm 1rr),2,1(NkQqTqTdtdkkkkkqVQ22kkkqVqTqTt)(dd),2,1(,0),(21NkqVqqqtVVkN 0)()(ddkkkkqVqTqVqTt0)(ddkkqLqLt2324OARr2222212121AAAOJvmJT2221)(92(121rRmmrrRrvrRvAAA)(25OARr2222212121AAAOJvmJT2221)(92(121rRmmMMWQFQTTt)(ddMrRmm 221)(92(61221)(92(6rRmmM 002221)(92(3ttrRmmM26CROxx22221212121CCJvmxmT2221RmJRxvCC222222143)(21RmxRmxmmgfmmFxxFFxWQsFx)()(2100，x00，x0FWQ27xQxTxTt)(dd RmxmmxTdtdRmxmmxT221221)()(gfmmFRmxmm)()(21221 QTTt)(dd 2222222323RmxRmxTRmxRmT023222 RmxRm3)(2121mmgmmfFa解得：解得：222222143)(21RmxRmxmmT0QgfmmFQx)(212829222121CCJmvTcos2sin2lylyCCsin2cos2lxxlxxCC)31sin(2121)cos21()sin2(21222222llxxmJlxmTC)cos2(212lxmgkxV30)cos2(212lxmgkxVTL)31sin(21222llxxm2121,2,1,qxqqxqkqk广义坐标广义坐标0)(ddkkqLqLt31mgxkxxLsin21lmxmxLcos21sin21)(dd2lmlmxmxLt )cos2(212lxmgkx)31sin(21222llxxmVTL0)(ddxLxLt0cos21sin212mgkxmlmlxm 320)(ddLLtcos21sin213)(dd2lxmxmlmlLt sin21cos21mgllxmLsin21312xmlmlL0sin21sin213gxl 0cos21sin212mgkxmlmlxm )cos2(212lxmgkx)31sin(21222llxxmVTL33OACkxxy34OACkxxy22222121212121CCOOJvmJxmTsin2cos2lylyCCcos2sin2lxxlxxCCcos212122glmkxVcos2161)23(412222221x lmlmxmmT35OACkxxy0)(ddkkqLqLtVTLcos2161)23(412222221x lmlmxmmcos212122glmkx2121,2,1,qxqqxqkqk广广义义坐坐标标36kxxLcos21)23(21221lmxmmxLsin21cos21)23(21)(dd22221 lmlmxmmxLt0)(ddxLxLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos)23(22221kxlmlmxmm 37sin21sin2122glmxmLcos2131222x lmlmLsin21cos2131)(dd2222 x lmx lmlmxLt0)(ddLLtcos2161)23(412222221x lmlmxmmVTLcos212122glmkx0sincos32gxl 0sincos)23(22221kxlmlmxmm 3839222222112121212121OOOOOOJmvJmvT11,3OORv232,3222RvvRvRvrOErOrOErcos1249cos22222221222122RRRvvvvvrOOrOOO40222222112121212121OOOOOOJmvJmvT11,3OORv2322RvvrOErOcos1249cos22222221222122RRRvvvvvrOOrOOO)cos1(641822222mRmRmRcos2mgRV410)(ddkkqLqLtVTL2121,2,1,qqqqkqk广义坐标广义坐标)cos1(641822222mRmRmRcos2mgR420L)cos1(63622mRmRLsin6)cos1(636)(dd2222 mRmRmRLt0)(ddLLt0sin)cos1(62 cos2)cos1(641822222mgRmRmRmRVTL43sin2sin62mgRmRL)cos1(6822mRmRLsin6)cos1(68)(dd222 mRmRmRLt0)(ddLLt0sin)cos1(34Rg cos2)cos1(641822222mgRmRmRmRVTL0sin)cos1(62 44广广义义动动量量jjjjpconstpqTqLEVT45)cos1(641822222mRmRmRTcos2mgRVcos2)cos1(641822222mgRmRmRmRVTLconstgRcos2)cos1(3922constLL,0const)cos1(646constgRcos2)cos1(3922const)cos1(60sin)cos1(34Rg 0sin)cos1(62 474849)21(0)(nimiiiii,raF 50),2,1()(NkQqTqTdtdkkk),2,1(0)(NkqLqLdtdkk51广广义义动动量量jjjjpconstpqTqLEVT52
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