55)在离心节速器中,质量为m2的质点C沿着一竖直轴运动,而 整个系统则以匀角速绕该轴转动试写出此力学体系的拉氏函 数,设连杆的质量均可不计 解:自由度为1选广义坐标为6 JXB-asin 0, xp=asin O,xc=0 [=B=acos, =D=acos 0, =c=2a e vn2 4 B D=acos60元 0 zn=/2=-asi660 E v=V+Qxr=(xi +ij+ik)+(Qk)x(xi+yj+zk 求得v2=vb=ab2+ga2sin2,v2=4a2sin2b 势能 V=-2ga(m+m2,)cos 6 L=T-V=m,a(6+Q2 sin 0)+2m,a sn 80+2ga(m, +m,)cos e5.5)在离心节速器中,质量为m2的质点C沿着一竖直轴运动,而 整个系统则以匀角速绕该轴转动.试写出此力学体系的拉氏函 数, 设连杆的质量均可不计. 解:自由度为1.选广义坐标为     = = = − = − = =     = = = = − = =              / 2 sin cos , 0 cos , cos , 2 cos sin , sin , 0 z z z a x x a x z a z a z a x a x a x B D C B D C B D C B D C 由 v V r (xi yj zk ) ( k ) (xi yj zk ) r               = + = + + + −  + + x z 求得 2 2 2 2 2 2 2 2 2 2 2  sin , 4 sin    vB = vD = a + a vC = a 势能 V = −2ga(m1 + m2 )cos ( sin ) 2 sin  2 ( 1 2 )cos 2 2 2 2 2 2 2 2 L = T −V = m1 a  + + m a  + ga m + m