刚体平面运动的矢量导数解和矩阵解

The Vector Derivative Solution and Matrix Solution of the Plane Motion of A Rigid Body

一般而言，在理论力学的运动学中，平面运动刚体的平面图形上各点的速度与加速度的主要求解方法与计算公式，是应用运动的分解与合成─Ｃｈａｓｌｅ运动叠加定理导出的。本文作者应用矢量导数直接导出上述公式，并且在矢量导数的定型公式基础上建立相应的定型矩阵公式，使此类问题的求解简明便捷，又能应用矩阵的ＦＯＲＴＲＡＮ程序，使用日趋普及的现代化电脑进行运算。

Generally, in 'Theoretical Mechanics',the derivation of formulas to calculate the velocity and acceleration of arbitrary points in the plane figure of a rigid body in plane motion is merely based on Chasle's Theorem of superposition of motion.In this article,however,the author derived the above mentioned formulas directly through the method of vector derivations and also set up corresponding matrix formulas that can easily be solved by the application of a computer.