平面运动刚体相对于某一点的转动微分方程及应用

A DIFFERENTIAL EQUATION OF ROTATION WITH RESPECT TO A SPECIFIC POINT OF RIGID BODY EXECUTING PLANAR MOTION AND ITS APPLICATION

本文系统地证明了在一定条件下,对于I_e·d^2?/dt^2-=∑M_e(F_?)形式的转动微分方程不仅对固定轴和质心成立,而且对速度瞬时中心和加速度瞬时中心均成立。进一步证明了对于平面运动刚体任何加速度指向质心的点均成立,这些点的轨迹为一条通过质心的圆。最后,本文推导出刚体平面运动微分方程的其它形式,即二矩式和三矩式。

The theorem of moment in the form of I_e d^2φ/dt^2=ΣM_e(F_1) which has been com-monly used in determining angular acceleration of a rigid body cxecuting plan-ar motion may be applied to fixed axes or centers of mass. Systematic analy-ses show that the theorem of this form applies to a instantaneous center of zeroacceleration and centers of zero velocity under certain conditionds as well. Fur-ther study proves that I_e d^2φ/dt^2 =ΣM_e(F_1) is valid for all points on the bodythat is accelerating directly towards or away from the center of mass, and thesepoints happen to form a circle passing through the center of mass. Finally,other types of differential equations for the planar motion of a rigid body,two - moment and three - moment types,are deduced.