理论力学全套解疑18

y18-21ABPCQylωAOC=ϕϕωyABCABGϕωsin2lan=AGBanϕωsin2lgPagPGGnBA===Oδϕ18-2111930])()[(1=+++∑=iiyiyiixixniyGFxGFδδ0][])()[(])()[(=+++++++++CyCxBByByBBxBxAAyAyAAxAxyQxQyGPxGPyGPxGPδδδδδδ0sin;0sinsin2,0sin,cossin,coscos20;cossin;cossin;0;0;022===−=−==−==−=−======−=======ByBxAyAxCCBBAACCBBAAyxByBxAyAxGlgPGGlgPGlyxlylxlylxlyxlylxlylxQQQPPPPPPϕωϕωϕδϕδδϕδϕδϕδϕδϕδϕδϕδϕδϕϕϕϕϕ0)sin/2()sin()cos(sin/)sin()cos(sin/22=−+−+⎟⎟⎠⎞⎜⎜⎝⎛+−+−⎟⎟⎠⎞⎜⎜⎝⎛ϕδϕϕδϕϕδϕϕωϕδϕϕδϕϕωQlPlgPlPlgP0)(cossin22=⎥⎦⎤⎢⎣⎡+−δϕϕωϕQPgPllδϕ0)(cossin2=⎥⎦⎤⎢⎣⎡+−QPgPlϕωϕϕ0)(cos2=+−QPgPlϕω194gPlQP2cosωϕ+=ωcosϕϕ20)()[(11=⋅+⋅=⋅+∑∑==iiiiniiiinirGrFrGFδδδ0=⋅+⋅+⋅+⋅+⋅CBBBBAAAAQrrGrPrGrPδδδδδ0180cos||cos||)90cos(||cos||)90cos(||=++++++DDDCBBBBAAAAQrrGrPrGrPδϕδϕδϕδϕδPA=PB=P0||cossin2sin22=−+−CQllgPPlrδϕδϕϕωϕδϕϕδϕδcos||)290cos(||CArr=−Dϕδϕδsin2||lC=r0)(cossin22=⎥⎦⎤⎢⎣⎡+−δϕϕωϕQPgPllgPlQP2cosωϕ+=19514-142AaOCAaaRgPAG−=OεOCaOOOGJMε=CCCGgPaR−=ε18-22εCCGJM=18-22A)|(|xAAδδδ=rrO⎟⎠⎞⎜⎝⎛=rxOOδδϕδϕCPdϕCδxC⎟⎠⎞⎜⎝⎛==rxRxC4δδδϕδϕ0)()(1=−+−−−δϕδδϕδCGCCGOOGAGMxRFMxRPagPagPRagrPragrPJMagPRCCGOOOGAG2222===⋅===ε22212kxkxFagrPRagPRJMCCOCG===⋅==ε19608154=⎟⎟⎠⎞⎜⎜⎝⎛−−xagPkxPδδx08154=−−agPkxPAgPkxPa15)4(2−=qj0)(1=⋅−∑=iiiinimraFδ0)(*1=⋅+∑=jjjkjqQQδ⎥⎥⎦⎤⎢⎢⎣⎡∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂−=∂∂⋅=∑=jjjjiinijqTqTtQqQdd*1rFj=1,2,,kqj2121iinivmT∑==197kq1q2qkkδq1δq2δqk0)(*1=⋅+∑=jjjkjqQQδj=1,2,,k0*=+jjQQjjjQqTqTt=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂ddδqjδqj0)(1=⋅−∑=iiiinimraFδ19814-1421jjjQqTqTt=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂ddj=1,2,,kAxq=xT18-51222222222221615/222122221221212121xgPRxgPRxgPrxgrPxgPJvgPJvgPTCCOO=⎟⎠⎞⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛+=⎟⎟⎠⎞⎜⎜⎝⎛+++=ωω18-51xQxAδxCδxδxC199422kxPxxkxxPxwQxx−=⎟⎠⎞⎜⎝⎛−==∑δδδδδxQxTxTt=∂∂−⎟⎠⎞⎜⎝⎛∂∂dd40815ddkxPxgPt−=−⎟⎟⎠⎞⎜⎜⎝⎛gPkxPxa15)4(2−==20dd=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂jjqLqLtj=1,2,,kCTV15-815-822281)2(221])([kxPxPrhxkPxrhPPhVVV+−+=⎟⎠⎞⎜⎝⎛+−++=+=2281)2(1615kxPxPrhxgPVTL−++−=−=0dd=∂∂−⎟⎠⎞⎜⎝⎛∂∂xLxLt20004815dd=⎟⎠⎞⎜⎝⎛−−⎟⎟⎠⎞⎜⎜⎝⎛kxPxgPt015)4(2=−==PkxPxa15-2m12aOAm22bABAO18-52tθϕ18-52q1=θq2=ϕT⎟⎠⎞⎜⎝⎛1++=+=22222222121ABCCOAOABOAJvmJTTTωωOAO212134)2(31amamJO==OAOθω=OAABC2201)cos(44dcoscos2(ddsinsin2(ddddd222222222222θϕϕθϕθϕθϕθ−++=⎥⎦⎤⎢⎣⎡++⎥⎦⎤⎢⎣⎡+=⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎟⎠⎞⎜⎜⎝⎛=abbatbatbatytxvCCCABC2222231)2(1212bmbmJC==ABϕω=AB)cos(2323222222221θϕϕθϕθ−++⎟⎠⎞⎜⎝⎛+=abmbmammTVL)coscos2(cos)cos(23232)coscos2(cos212222222121ϕθθθϕϕθϕθϕθθbagmgamabmbmammVTLbagmgamV+++−++⎟⎠⎞⎜⎝⎛+=−=+−−=0dd0dd=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂=∂∂−⎟⎠⎞⎜⎝⎛∂∂ϕϕθθLLtLLtϕθϕθθϕθϕθθϕϕθϕϕθsin)sin(2)cos(234sin)2()]sin()cos([2432212221gaabmmgbmamm−=−+−++−=−−−+⎟⎠⎞⎜⎝⎛+2021234qjQjjQ′jjqVQ∂∂−=17-83jjjqwQδδ′=′∑17-82jjjjQQqTqTt′+=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂ddjjjjQqVqTqTt′=⎟⎟⎠⎞⎜⎜⎝⎛∂∂−∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂ddjjjQqLqLt′=∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂dd203L2amABA18-6(a)BFCCρk18-61l0OOxy18-6(b)xQθ==21,qxq2])(cos2[2121d)cos(dd)sin(d212dddd21212122222222222222θρθθθρθθθρω+++=+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡+=1+⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛=+==axaxmmtataxmmtytxmJmvTTCCCC3VθQQx′′204θδθθδθδθδδθδδδδδθθθcos2cos321)cos(2aFaFxFxwQFxFxwQkxaamgVVVBxx−⋅==′=′−=′=′+−=+=∑∑4θθθθQVTTtQxVxTxTtx′=⎟⎠⎞⎜⎝⎛∂∂−∂∂−⎟⎠⎞⎜⎝⎛∂∂′=⎟⎠⎞⎜⎝⎛∂∂−∂∂−⎟⎠⎞⎜⎝⎛∂∂ddddθθθθθρθθθcos2sinsin])(cos[dd)cos(dd22aFmgaxmaaxamtFkxaxmt=++++=++θθθρθθθθθcos2sin])(cos[)sincos(222aFmgaaxamFkxaaxm=+++=+−+qjj=1,2,,ktk12T205qjQj345206