理论力学全套解疑16

·GmaaGm−=GeGkaeakkkeemmaGaG−=−=16-6······14-141··16-71PPPXOYONF1ABAGR⎟⎟⎠⎞⎜⎜⎝⎛←=↑=agPRagPRBGAGBGROOOOGGgrPJMMεε2(200==agrP2=)XOYOOBN=PO0)()(,0)(01=+++−−=∑GBGAGOMrRFrRPmF16-7116-72F1=kxgPkxPa5)(2−=aXOYO0,00,01=+−−−+==−−=∑∑AGOyBGOxRPPPNYFRFXFa528532kxPYkxPXOO+=+=AB16-72A001=−+=∑PTRFAGya5231kxPT+=B00=−=∑PNFyN=P0012=−−=∑BGyRTTF5322kxPT+=1·2·3+16-72AOB1+3+2=6A0,01=−+=∑PTRFAGyO000000)(1221=′−−==′−==+′+′−=∑∑∑TPYFTXFMrTrTmOyOxOGOFB000012=−−==−=∑∑BGxyRFTFPNFPNkxPYkxPXkxPTkxPTgPkxPaOO=+=+=+=+=−=5285325325235)(22114-141·A14-142A14-14216-8C14-141FO03,0)(1=−−+⋅+++−=∑rRrFMrFMrRrPmCGCGOGAGOF=⋅==⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛==CGCCGOGAGRxkFagrPRaRgPMrrgPMagPR2222122a⎟⎠⎞⎜⎝⎛2agP02323=−−+kxPFagP(1)14-1414-41(1)(1)aFAa16-816-9·14-142·++1+16-8(1)FkxPagP3223−+=(1)C16-90,012=−−+=∑CGxRFFTFFgPakxT−+=222(2)02,0)(0,012=+++⋅−==−=∑∑CGCGPyMRRRFTFPNFRF(3)kxTagP−=2423(4)(1)(2)(3)(4)aT2FNPNkxPFkxPTPkxPa=+=+=−=3072515)4(22O(5)0,0)(102=′−+′=∑rTMrTmGOF(6)0,02=′−=∑TXFOx0(7),01=′−−=∑TPYFOy52220kxPTTagrPMG+=′==(5)(6)O15222515271kxPYkxPXkxPTOO+=+=+=′2+AOC16-9⎪⎪⎭⎪⎪⎬⎫=′−−==′−==′−+′==−+=∑∑∑∑0,00,00,0)(0,0121021TPYFTXFrTMrTmPRTFOyOxGOAGyF⎪⎪⎭⎪⎪⎬⎫=−==−−+==+++⋅−=∑∑∑0,00,002,0)(1212PNFRFFTFMRRRFRTmyCGxCGCGPF77aT2FNT1XOYOmCωεOeOC=16-10116-1022ωετmeRmeRnGG==εOGJM=016-10116-10216-102CGmaR−=RG−maCRGCRG=−maCRGmaCRGaCRG=−maCORG=−maCOO0GM=−=∑∑)()(aGmmmOOεOJ−16-10316-10316-10416-105ORGCC⋅e16-10416-105τGRτGRεετ2meeRJMGOOG=⋅=CGCOOMJmeJmeJ==−=−+εεεε)()(2216-1051ORG=−maCτGRεττmemaRCG==nGR2ωmemaRnCnG==Oεε)(20meJJMCOG+==e16-1032CRG=−maCOOCε16-105τGRnGRεOCGJM=16-102CεOGJM=016-1116-11(a)LPABABOzθω=BD·ABAzxyzJJXAZAABPT16-11bOzOza=xω2xAB16-11bTA0cos2sin,0)(=−⋅−⋅=∑AGAMLPLTmθθFAAABAldl16-11cdmAAGM2cosddωθ⋅⋅=lmGθθωθθωθcossindcossindsindd2222llLmlmlGMAG⋅=⋅=⋅=gPm=ABAθθωθθωcossin31dcossind22220mLllLmMMLAGAG===∫∫16-11A0cossin31cos2sin22=−−⋅θθωθθmLLPLTθωθcos3ctg22LgPPT+=TAXAZA00==∑∑zxFFG=maCABCG16-11dAGML=⋅θsinGLgPLLgPL32sincos2cossin3222==θθωθθωABGA·mrOO16-121CONO116-122eCmFa∑=mgYaamFmaXaamFmaOCynCyeyCyOCxnCxexCx−=+==+=∑∑)(,)(,ττmgYrrmXrrmOO−=−−=−)sincos()cossin(22ϕεϕωϕεϕω(1))cossin(2ϕεϕω−=mrXO(2))sincos(2ϕεϕω+−=mrmgYOωε)cos(212ϕωrrmgOJO−=−(3)ϕsinrmgeJO⋅=(4)223mrJO=(3)(4))cos1(342ϕω−=rgϕεsin32−=rgω2ε(1)(2)OC2π=ϕNOxymgYmgXOO3134==COmgmgmgYXNOOO31731342222=⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛=+=16-12216-1232··OCO16-123τGRnGROGM(5)0sin,0)(=−⋅=∑OGOMrmgmϕF(6)0sincos,0=−+=∑ϕϕτnGGOxRRXF(7)0cossin,0=++−=∑ϕϕτnGGOyRRmgYF2223ωεεεττmrmaRmrmaRmrJMnCnGCGOOG======(5)ϕεsin32rg=ϕωωωεdddd==t)cos1(342ϕω−=rgεω2(6)(7)nGGRRτ2π=ϕmgYmgXOO3134==··⎟⎠⎞⎜⎝⎛=2πϕ16-1316-1300)(=−⋅=∑OGOMrmgmF(1)00=−=∑nGOxRXF(2)00=−+=∑mgRYFGOyτ(3)2223ωεεεττmrmaRmrmaRmrJMnCnGCGOOG======mgYmrXrgOO31322===ωεXOωmgrJO=−0212ωrg342=ωXOmgrgmrmrXO34342=⎟⎠⎞⎜⎝⎛==ωO2π=ϕεωXOYOεωr2lOAOOA16-141mαµv0s16-142sFrvmrmvmvOA−=⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛++−0220202121212116-141OAmgNNPA2=+mgNA21=mgNFAA21µµ==gvsµ2520=⎟⎠⎞⎜⎝⎛+=αµµtg22520gvsFA=µNANAsNAsNAOOa16-142aOAOAmgNA21=NAaOAO16-14316-14216-1431OA16-143a0)(=∑FAm0sincossin2cos2=−−⋅−⋅ααααlRmgllXlYGOO(1)(2)0,0=−+=∑mgNYFAOy(3)0,0=+−=∑GAOxRFXFmaRNFGAA==µ2O16-143b(4)0)(,0)(=−−=∑OGGOPMrRXmF(5)0,0=−−=∑mgYNFOPy(6)0,0=−−=∑POGxFXRF2212mraramrJMOOG=⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛==ε66XOYOaNANPFP(1)(2)(3)(4)=+=++−+=+++=+−+−=)tg45)tg2(1tg2)tg1(2)tg2(1tg)tg1(21)tg2(1tg)tg1(21αµµαµαµαµµαµααµαµααµgamamgXmamgNmamgmgYOAOasvvtssvtv−===ddddddddsavvsOOvdd0∫∫−=asv=220sgvαµµtg45220+=⎟⎠⎞⎜⎝⎛+=αµµtg22520gvs123aXOYOaNANPFP·zzCCxyz16-150==∑mzxJzx0==∑myzJyzOzzz′Ox′y′z′0=′′=∑′′xzmJxz0=′′=∑′′zymJzyzOJz′x′=0Jy′z′=0OOx′CxOy′Cy16-16mMxyzx′y′z′x′=xCOzzyy+=′=′,0)(0)(=⋅+=⋅+=+=′′==+=⋅+++=′′=∑∑∑∑∑∑∑∑′′′′CyzzyCzxxzMyOCJOCmymyzOCzmyzymJMxOCJxOCmzxxOCzmxzmJ12