理论力学全套解疑14

MlωOOAKvm∑=MvvKm∑=CvCC14-11KKCmmvvK==∑KCKMvCmvK=CK=MvCKvCKCOAOω14-12KK=MvCMvCvCKCl32C114-12CCCCmmvvK==∑ωCCCJmmH==∑)(v14-13HC0CK=MvCOAKKHCC1K14-1(4)14-1(5)14-1214-1314-14K″=KK′=MvCK″⋅d=HCllMMlMvJKHdCCC612/12/2=⋅⋅⋅==′′=ωωωKC1OlllOC3261211=+=14-1414-1512OAO2lMvHCO⋅=OAO2lMvHCO⋅=14-1114-15ωOOOJmmH==∑)(vlvlvMlJCCO22/,312===ω322312lMvlvlMHCCO⋅=⋅⎟⎠⎞⎜⎝⎛=ω32MlHO=O∑=)()(KvOOMmmOAOlMvlMmmHCOOO3232)()(⋅=⋅===∑KKv2lMvHCO⋅=CKK1ωOOJH=2F,F′14-3CzF,F′FF′vFa∑=CM0=CaCCCCz00=Cv0=Cv14-3P1P2ADBDDAB14-41D1P1=P222121PP=1P1=P214-4114-4214-42xCx0=∑exFexCFxM∑=C=DxDCxCxD=DvD14-4222121PP=14-431xC=P2P1CC1C2C2CxCCD14-43D14-4314-5Fv=tmd)(d(1)mvMF14-5(1)dt(2)tmmtd012Fvv∫=−(2)F0tFttd0F∫FmvmOOtm=d)]([dFrvr×=×tmd)](d(3)rM14-5tmmOtOOd)()]([)]([012Fmvmvm∫=−(4)tmmtd)()()(01122Frvrvr×=×−×∫(4))d(d)(00ttttFrFr×=×∫∫Frr21-3vpv114-6∆tFvvgpv11vgptFvgpvgp∆=−1FtgvvpF∆−=)(21v1F=maavva=ve+vrvevrvr=v1vevv′v′vv′100.6900/0.054/Fve=vvgpv+v1)(1vv+gptFvgpvvgp∆=−+)(1tgpvF∆=1zJ14-7amv0O1rlOO=1M0ω0Mωωϕ=M0O1M14-7a0)(=∑ezFmzM0)()(0000rlmvrlmvJHMz+=++=ω14-7M14-7brmvlmvJrlvmrvmJHMz0000cos)cos)(cos(sin)sin(++=+++=ϕωϕϕϕϕω0MzMzHH=Jlmv)cos1(0ϕω−=zMzv014-7c14-7d[])()()()(reavvvvmmmmJmmJmmHzzzMzMz++=+==∑ωω14-7rmvlmvrmvrmvlmvrvmrlvmvmrlmmmmmmmlrrlmOMmOMOMmOMmvmmzrzzz0020200rrrrrr222eecossincoscossin)sin()cos)(cos(sin)cos()()()()]180cos(2[)()()(+=++=++=′′++′=′′+′=−−+==⋅=⋅=ϕϕϕϕϕϕϕϕϕϕϕωωωvvvvvDrmvlmvlrrlmJHMz0022cos)cos2(+++++=ϕϕωω[])()()(00000rlmvrlmvJmmHMzMz+=++==∑ωv0MzMzHH=)cos2()cos1(220ϕϕωlrrlmJlmv+++−=(a)QrOJPM14-8rPMJ−=εJprM−=ε∑=)(FzzmJϕ14-8a()[]()∑∑=emtFmvm00dd14-8b,OO()rvgPJmm⋅+=∑ωv0()∑−=rPMmeF0rPMrvgPJt−=⎟⎟⎠⎞⎜⎜⎝⎛⋅+ωddωrv=εω=tdd2rgPJrPM+−=ε123PS14-9b14-8(a)14-9b14-9cSrMJrTMJ−=′−=21εεε1ε2T′ST′Tε1ε2TSS=Pε1ε2TP14-9bPTagp−=gpaR=TPTP0TPε1ε214-9PM21rgPJrPM+−=εPSJrPM−=2ε14-8(a)εm14-101IM0J1J2z2/z1=kR14-101O1O1O2O214-10214-103M0P1P2PFF′2211OOOOYXYX1011cosrFMJ⋅−=αε(1)14-10214-103O2PRrFRmvJt−⋅′=⋅+222cos)(ddαωmgRrFmaRJ−⋅′=+222cosαε(2)r1r2kzzrr===121221ωωω1=kω221εεk=(3)aa=Rε2(4)F′=F(5)(1)(2)(3)(4)(5)21220)(JJkmRmgRkMRa++−=nCnCFMaFMa∑∑==,rr14-12ABlM14-12aAAz′231lMJA=DDz″2222973231lMlMlM=⎟⎠⎞⎜⎝⎛+=ADMJJAD+=297lMJD=AB14-12b222222913611212132121lMlMlMllMlMCDMJJCD=+=⎟⎠⎞⎜⎝⎛−+=+=2121lMJC=2ACMJJCA+=2222121231lMlMlMACMJJAC=⎟⎠⎞⎜⎝⎛−=−=MRω14-131Oωω2MRRMR=⋅=RMvHCO⋅=O)(vmmHOO∑=OKv()(OOmmm=∑KOKHOKMvCCCCCmmvvK==∑ωCCCJmmH==∑)(v14-132a14-114-135KHCC1K14-132bc22/2RMRMRMvJKHKHdCCCC====′′=ωωω,OKRRRRd232=+=+Oω22323()(MRRmvmmmHCOOO====∑Kv14-132CmmvvK==∑KC14-14114-142AxaO14-141a=gPkxP5)(2−14-142gPkxPa15)4(2−=1ABOPrkl014-141Axa14-14114-1422ACOPrRR=2rkl014-142Axa114-14114-143NXOYOByaBy=0N=PXOYOOXOYOOPF1OrvgPJrvgPOO⋅⋅,,ωOrFrPrvgPJrvgPtOO1dd−=⎟⎟⎠⎞⎜⎜⎝⎛⋅++⋅ωkxFrvrgPJOO===12,,2ωtvadd=gPkxPa5)(2−=Aa214-14214-144BC14-143CF14-144CFFfN4NFXOYON=PFXOYOOXOYOF14-143FOAOrvgP⋅JOωOCOCCK=MvCHC=JCω14-14314-14414-142OACO02)2(22=⎟⎟⎠⎞⎜⎜⎝⎛⋅−⎟⎟⎠⎞⎜⎜⎝⎛=rvrgPrvgPHCCOOrFrFrPOJrvgPtOO3dd1⋅−+=⎟⎟⎠⎞⎜⎜⎝⎛++⋅ωatvxkFrvrgPJOO====dd2212ωFxkPagP3223−+=(1)(1)aFGRS14-15aGlABAByx14-15bFNNANBPSRJtP=)(dd1ω(1)ϕωcos2)(dd2lGJtABP⋅=(2)14-15(1)(2)FRJtC=)(dd1ω(1)′ϕϕωsin2cos2)(dd2lNlNJtABABC⋅−⋅=(2)′FNANBPJSRt1dd−=ωεPABABJlGt2cos2ddϕωε==PC15-7O′O′O′CC⎪⎭⎪⎬⎫==∑∑)()(ddeCCeCmJtMaFFω⎪⎪⎭⎪⎪⎬⎫======∑∑∑)(eCCCeyCCyexCCxmJJyMMaxMMaFFFϕεC