平面运动刚体动量矩定理矩心的选择

Choosing the Moment Center of Angular Momentum in the Rigid Body with planar Motion

本文讨论了平面运动刚体成立动量矩方程ｄＧ／ｄｔ＝Ｌ的矩心选择问题，除可选在刚体质心，加速度瞬心上外，还有许多可供选择的点，这些点组成了ａｃ／２ε为半径，且过刚体质心Ｃ与质心加速度ａｃ相切的一个圆周，称之为矩心圆。刚体质心和加速度瞬心均为该圆周上的一个点。同时分析了平面运动刚体速度瞬心在矩心圆上的条件，即相对于速度瞬心ｐ成立ｄＧｐ／ｄｔ＝Ｌｐ的条件。为平面运动刚体的动力学分析提供了便利的手段。

In this paper we have discussed the problem of selecting the moment center about which holds the relative equation of angular momentum dG/dt =L. Besides the center of mass and the instantaneous acceleration center of the rigid body, there are a lot of other points for choice. These points compose a circle which is called the circle of moment center in this paper. The circle,with a radius ac/2ε, passes through the center of mass and the instantaneous acceleration center of the rigid body and the acceleration vector of the mass center a. is one of its tangents.We have also analysed the condition of the instantaneous velocity center being on the circle of Moment center,or the condition of the instantaneous velocity center about which holds the relative equation dGp/dt=Lp. The analysis provides a useful mean in solving the dynamics of rigid body with planar motion.