刚体空间运动的动力学方程的联合推导

United Derivation of Dynamical Equations for Rigid Body Spatial Motion

摘要: 本文推导出相对任意基点刚体动力学方程的一种更简洁的形式。推导过程是以质点系动力学理论为基础的，它是一个比动量定理和角动量定理更基本的理论前提。在现有的动力学方程中，线加速度和角加速度是相互耦合的，这导致了求解方程极其困难，特别是在高速旋转的条件下。本文通过平移方程和旋转方程的联立推导，将线加速度和角加速度解耦。基于推导过程，讨论了与现有形式的关联，陈述了与现有推导过程的主要差异。

Abstract: Dynamical equations for rigid body spatial motion are derived from Dynamical equations of system of particles, which is a more fundamental theoretical basis than the momentum theorem and angular momentum theorem. Linear acceleration and angular acceleration are coupled with each other in the present dynamical equations which lead to solve the equation is extremely difficult, especially under conditions of high speed rotation. The derivation coupled the translational for-mulation and the rotational formulation, and uncoupled the linear acceleration and angular ac-celeration. Based on the derivation process, the relationship between the equations and the exist-ing forms is discussed; the main differences from the existing derivation process are stated.