理论力学(30-30)-作业资料

1-2ABlB=ts=a+bsintabAABABOxytxxlylABA=+=sin,cosϕϕxsabB==+sinϕAxablylAA−++=2211-3rv0°=30θMyxM0=x22002022)(tvtrvtvrry−=−−=y20022002vrvtyrvtvt−=−122002200220022002022/)(2tvtrvtvtrvtvrvtvtrvvy−−−−−−=230=θrtvr230=−rtv)231(0−=120303|vy==θrry20308|−==θ1-5OO1=l=0tD°=30θDxyCDOOC1/2lDcos2sin2lxlyθθ==2θϕ=D00sincossincos22llxyllθθθθωθωθ=+=−+=−+vijijij22002cos2sinxyllωθωθ=+=−−aijij30ϕ°=60θ°=D2200(sin60)(cos60)vlll0ωωω°°=+=222200(2cos60)(2sin60)2alll20ωωω°°=+=1-12ABAtωϕ=ωBABR=10cmO1BB1-12O1BsBnτ2sRRtθω==2sRω==υττ22R4ssRω=+=τann()0.1radsωπ=(10cmR=)2cstπ=()m()2cmsπ=υτ()22s0.4cmπ==an1-14QQ'OABtωϕ=BO=AO=aAMbMBBOM()()=+=tttabtωϕωρcos2()()tabtϕρcos2+=ρρ=vϕρϕ=v2ϕρρρ−=aϕρϕρϕ+=2atabbavvvωωϕρcos442222++=+=tabbaaaaωωϕρcos81622222++=+=1-17Mrtsrmt=3sMkji)3/()3()7(32ttt+++=M272xyztt=++=++vijkijiiik22xyzt=++=+aijkjiiiiiik∵()()dddstdtdsdt===rrvτiss()sτ∴22222()7(2)4stxyzt==++=++viiiit∵sτ=aτii2ns=ρani22naaaτ2+=∴224332242(7(2))1(84)7(2)2dttdsasttttdtdt−τ++====+++iii22naaaτ=−t=33|769t==++vijkm/s,332242331|(84)7(2)|5.122ttttt−τ===+++=at(m/s2)2222233|(2(2))|3.71nttaaata=ττ==−=+−=(m/s2)2-4OAOrCEsradO/5.2=ω51=cmr152=AcmBD⊥EBADCB0=BvOA0ω120()50/Arrcmsω=+=vττ110(1)Avsrω==BAA=+×vvωrB5AB=rn505×=−=−τωn10τ100τ5050=+ττn5050=−ττn5050DAAD=+×=+=vvωrττ505EAAE=+×=+×vvωrτω505CAAC=+×=−×vvωrτω50/0100/70.7/ABDCEvcmsvvcmsvvcm=====sθvrωrr2-7OAωω=eBABωω4=rrr3OP=B,er=+=×+vvvωrvrrrvrrωω4==rveω10=,31−−=tgπθB°=90ϕϕDABω2rvABB×=ωrvvvvvererωθ23cos222=++=2-8OABO1ABBO211==OAOAsrad/3=ωOOOBO11ABB12-8ABABBAAvBvABωBAABAB=+×vvωr902sin30ABArvω⋅=D)/(330sin23sradrrAB==DωD30cos)/(2.530cos2sradrrABB=×=ωωD2-11aCDAB2==,cBDAC2==acBD2-11xyOPBDADADBADC∆≅∆CDADAB∠=∠PDPA=PCPB=aPBPDPCPA2=+=+PACDBPBDACACOACxOxy222221(xyycac+=≥−0)2-16,2-18,2-19,2-21,2-25,2-28,2-29,2-332-16vcmAB53.19=scmA/15=2/10scmaA=1ABB2ABB2-162-24eeerAB123,,e3AaABθωcmcm/scm/sAB,ε2rad/srad/s2227.51012.5AD=+=sin1012.50.8θ==cos0.6θ=12121sincos150.8150.6129AAAυθυθ=−−=−×−×=−−υeeeee2e2e32e12121sincos100.8100.686AAAaaθθ=+=×+×=+aeeeee212.5AD=re219.53AB=re21212912.5DDAADυω==+×=−−+×eυυωreee1212.50ω−−=0.96ω=−30.96=−ωe(1)()123211290.9619.536.759BAAB=+×=−−+−×=−υυωreeeee2e(2)(a)10cmh=cotxhθ=1()2222222hxxhxxhxhθ=−+++7.5x=cm15Axυ=−=−cm/s10Axa==cm/s2θ(a)EADxh2.02θ=rad/s22.02ε=32.02=εe(3)()22123221862.0219.530.9619.5331.4512BAABABω=+×−=++×−−⋅=−−aaεrreeeeee2e(4)12342-18RBBa2-182-5OC()2221121Clllrlrr21ωωω=−=−annnRrRl+=()222111CRrRRrRrrωω+=+−=−+ann2∞→ra2ωRB=ω−nOB2-19vOxyl0()xfy=ABAB0ω2-19BBxθϕωωsin2)(0020202lvvlvr−+=θωϕsincos0lvr=ϕωϕωθsincostan000lvl−=θtan=′y=dxdyϕωϕωsincos000lvl−ϕsinly=lyl−=2cosϕdxdyylyv02200ωω=−−0arcsin02200=−−+xyllyvωω32-21ABuOCOC=aOD=lC45ϕ=Dϕeρe2-21OCAeOAϕϕ=νe1rdOAdtρ=νe2A1Aeuρ=+=vvvj3123coslOAϕ=(cos)sincoscosldluudtρϕϕρϕϕϕϕϕ+=+eeee230cos2uullϕϕϕ===DC2cuavOClϕ==2-25CR=60O1A42-25AO1C1OAO1Rvvceω==211ωω==COveAOCAO1cneeCaaaa+−−=6sin6cos3cosπππτ2ωRaC=22ωRane=2ωRac=322ωτRae=aετCOe1=AO1342ωε=2-28rO'OAAOO'M2-28:O,M,OMOer=+vvv1AM*rvv5.0=0)2/3(=−revv**rve3×=ωrvω=erc=++aaaa2213erω=×an1nMAMO,MO221(/)rrrvrrθ=+anτ2n1τ52224crrω=×=−aωvnMO/MO/232(/)vrrθ=+anτ3n2τ232(/)vrrθ+nτ=213rω×n+(/221)rrvrrθ+nτ224rω−nMO,2)3/21(ωra=2-29OA0ωOrOAr3BO1=OBOB1°=∠30AOB1O23B1PBnBnBτ2-29OxOAPOA011y01013POPrωω==νjj1BPB1+PBrω=ννi211111322BOBBOBOBOBrrωω==+ντi11ωj3132110111113322OBOBBrrrωωωω=++rjiji102OBωω=()03ωω=−B46B11111221111133332222BOBOBOBOBOBOBOBOBrrrrεωεεωω=+=+−+aτni121jij5PPerc=++aaaa2013erω=−ai0c=a013Prω=νj1y1rra=aj20113Praω=−+airj6BP21PBBBrrωε=++aa1ji7567111122201111111333332222OBOBOBOBBBrrrrrrωεεωωωε−=+−+++ii2rjijji848120233OBεω=0ε=B91()021ωω=BO203321ωε=BO0=ε203ωω=3103jvωrp=()1120163jia+−=ωrp2-33ABvBrABvϕrrϕϕ2−=2ϕrr=72-33BA()()0122=+−=ϕρϕϕerdtdrerra()01,022==−ϕϕrdtdrrrrrϕϕ2−=2ϕrr=82-36OA11O1ωBvAB0lAB2-36ωε:ABOAABAA11OAaer=+vvvab=+×vvωrer+vv=b+×vωr(1)(1)OA1100.50.5lvlωω=+(2)102/vlωω=−(1)OA(2)1103()rvLω=−vcAaer=++aaaa211elω=an1n1OA1rra=an12cr=×ωvaABAB22abllεω=++aann32n3n211lωn+a+21rnr×ωv=223llεω+nn1AO22011083(/)833(/)vlvlεωω=−−2-38OAOmin300rn=253=z/600=z401=z502=zαOA0213zzzzαθ=00213rnzznzz=0020000136050(1)260(/min)4025rnzznnnnnnrzz=−=−=−==iin02-40IIIIOIIOabIIIOII123ω123ω1r2r2ω(a)()2312Ovrωr=+IIIIII212222Orrvrr3ωω+==1232332rrωωωω=−=(b)()2312Ovrωr=−IIIIII212222Orrrr3ωυω−==1232332rrωωωω=+=2-44IIIABIVcmcmcmcmIIIIIIABIII4.5rad/srad/sIII51=r5=22=r101=R2R3ω1ω92=ω43ωω43ω3ω2ω1IIIV2232432RRrωωω=+IIV1131431RRrωωω=−37(/)radsω=435(/)radsω=3-1.1alABAB=aMAB2Mb3c4d5ABeyxyx(d)(c)yx(1)AMBMl+=2222,()AMxyBMaxy=+=−+()2222xyaxy++−+=l,(2)y=0,(3)Oxrθ=θOxrθ=(4)OxRϕ=φOxRϕ=(5)2222()BAAABxxyl=−+=22AAxry=−()2222ABAryxyl−+=23-2ABPDW1AB2AB3D(1)(2)(3)3-3AOCOBBW1AO2OC3B4AOC3-512345612364539A(a)Aαsin2lxA=LlyA−=αcos2αδαδcos2lxA=αδαδsin2lyA−=*δαδlrA2=ααθsin)sin(Ll=+θα=θcos2lL=θδθδα2cos=(*)θδθδ2cos2lrA=BArrδδ2=BOAθδθδ2coslrB=θδθδ2cos2lrA=(b)AconsthctgxA+=θ0=Ayθδθδδ2sin/)(hxrAA==Bθδθθδθθδδδ2sin/)(sin/))sin/((hhxxrBAA=×===(c)Aθcos2lxA=0=Ayθδθδδsin2lxrAA==δθδlrB=θδθθδ2sincoslrA=θδθδsin2lrA=3-11ωPQOAOBaACECOC===αXAaBaPPYPQ2sinAxaα=−0Ay=2sinBxaα=0By=0Ox=2cosOyaα=2cosAxaδδαα=−0Ayδ=2cosBxaδδα