经典变质量问题的研究

:2003-05-23:2002(B).:(1964-),,,.,(,445000):,,.:;;:O313.2:A:1008-8423(2003)04-0081-04(VnC),,.,m=(t)(t)t(,t)..,,..,,,.11.1tm(t),SV(VnC),mu,tt+tm(t),V+V,m(t)mF(e),:(m+m)(V+V)-mV-mu=F(e)t(1)mV,t,t0,:ddt(mV)-dmdtu=F(e)(2)=Vrdmdt,(2):mddtV=F(e)+(u-V)dmdt=F(e)+Vrdmdt=F(e)+(3)(3),[1].u=0,(2):ddt(mV)=F(e),u=V,(3):mdVdt=F(e).1.2(3),:mdVdtm(t)t;F(e)m(t)m;Vr214200312()JournalofHubeiInstituteforNationalities(NaturalScienceEdition)Vol.21No.4Dec.2003=u-V()dmm(t);dmdtm(t),Ûm=dmdt,Ûm0,;Ûm0,;=VrÛm,,(),:,Ûm0,Vr,dmVr;Ûm0,Vr,dmVr.22.1tm(t),S,V(VnC),mu,tt+tm(t),V+V,,:(m+m)(V+V)-(mV+mu)=0(4)mV,(4):mV+(V-u)m=0(5)(5):mdV-dmVr=0(6)2.2(6)[2]:mdVm(t);Vr=u-V();dmVrdmm(t);,(3),F(e)=0(6).3,,,,:V(2):VF(e)=Vddt(mV)-Vudmdt=mVdVdt+V2dmdt-Vudmdt(7)ddt(12mV2)=mVdVdt+12V2dmdt,(7):VF(e)=ddt(12mV2)-V(u-12V)dmdt(8)(8):ddt(12mV2)=VF(e)-12V(V-2u)dmdt(9)dmdt,udmdt,12u2dmdt.,u=12V,,,.12u2dmdt(9)12V(V-2u)dmdt,:ddt(12mV2)=VF(e)+12u2dmdt-12(V-u)2dmdt(10):12mV22-12m1V21=W+12u2dm-12(V-u)2dm.(11)28()21.:()=()+()-().,Q,Q=12(V-u)2dm.(11):,[3].44.1,.,.tm(t),S,Û,tt+dtdmu=0m,t+dt,Û+dÛ.r,.tt+dt,mdm,.:ddt(rmV)=rF(e).(12):r=ri,V=Ûri+rÛj,F(e)=Fi(e)i+F(e)jj,rF(e)=r2Ûk,rV=(ri)(Ûri+rÛj)=rF(e)jk.(12):(m+dm)r2(Û+dÛ)-mr2Û=r2Ûk(13)(12)dmdÛ,rdt:dmdtrÛ+mr=F(e)j(14)4.2(13)(m+dm)r2(Û+dÛ)(m+dm);(mr2Û)m;rF(e)jdtmdm.(13).5,.,[4]..,,;,:rc=6miri6mi;,:md2rcdt2=F(e);,.66.1Vr,dmdt=-,,.tm(t)=m0-t,V,,Vr+V,dm,m(t)dm.(1):(3):(m0-t)dVdt=Vrdmdt=2Vr,384::dVdt=-Vr(m0-t),V|t=0=V0,:V=V0+Vrlnmm0-at(2):(6):dVdt=-Vr(m0-t),.(3):(10):ddt(mV2)=(V-Vr)2m-Vrm,dmdt=-m=m0-t:dVdt=-Vr(m0-t),.6.2,l,t=0m0,m=m0(1+t),,.(1):dVdt=lj-lÛ2j;F(e)=-mgsinj+(mgcos-T)j;dmdt=m0;u=0;V=lÛjmdVdt=F(e)+dmdt(u-V),j:ml=2mgsin-dmdtlÛ,sin,:+1+tÛ+gl=0.=g/l2(1+t),d2d2+dd+=0.,:=C1J0()+C2N0().J0()N0(),C1C2,.(2)tm,Û,dtdmm,tt+dt,mdm,:(m+dm)l2(Û+dÛ)-ml2Û=-mglsindtdmdÛ,ldt,dmdt=m0sin,:+1+tÛ+gl=0,.,,,,.:[1].[M].:,1986.[2].[J].,1989,8(11):1819.[3].[J].,1995(4):67.[4].[J].,1995(8):35.ReasachonClassicalMass-VariableProblemYANGJian-ping,LIYi-chun(HubeiInstituteforNationalities,Enshi445000,China)Abstract:Thispaperanalyzesanddiscussesclassicalmass-variableproblembyusingsomespecificexamplesthroughthelawofmomentum,thelawofkineticenergy,thelawofangularmomentum,thelawofmomentumconservation,themovinglawofmass-center.Keywords:classicalmassvariableproblem;lawofmechanics;movinglaw48()21