质心动量定理的推导是什么,
2个回答

设一质点系由N个质点组成,各质点质量分别为M1,…Mi,…Mn,对应位失为R1,Ri,Rn,则

M1d^2R1/dt^2=F1+ …+Fi+…+Fn

Mid^2Ri/dt^2=F1+ …+Fi,i-1+Fi,i+1…+Fn

Mnd^2Rn/dt^2=F1+ …+Fni+…+Fn

两边相加

M1d^2R1/dt^2+…+Mid^2Ri/dt^2+…+Mnd^2Rn/dt^2=Md^2((M1R1+…+MiRi+…+Mnd2Rn/dt^2)/M)/dt^2

=Md^2(∑MiRi/M)/dt^2

=∑Fi

令M=M1+…+Mi+…+Mn为系统总质量,则令Rc=∑MiRi/M

则Md^2Rc/dt^2=∑Fi

Vc=dRc/dt=d（∑MiRi/M）/dt

Ac=d^2Rc/dt^2=∑Fi/M

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