分析力学基本微分原理在刚体系统动力学中的应用

Application of the Basic Differential Theory of Analysis Mechanics in Rigid System Dynamics

本文试图把分析力学中已经发展成熟的基本方法应用于刚体系统动力学的研究。首先给出三类空间(坐标空间,速度空间和加速度空间)中刚体虚位移的定义,在此基础上,把分析力学的三个基本微分原理(D'Alembert—Lagrange原理,Bertrand—Jourdain原理和Gauss原理推广到适用于刚体系统、对有非线性非完整约束的刚体系统,应用Bertand—Jourdain原理推广了Wittenburg方程。应用Gauss原理,推导出有二阶非线性非完整约束的刚体系统运动方程。

This paper tends to research rigid system dynamics by the basic method that has been developed into maturity in analysis mechanics. First, the definition of rigid virtual displacement in three kinds of space (coordinate space, velocity space and acceleration space) is given. On this basis, three basic differential theory (D' Alembert-Lagrange Theory, Bertrand-Jourdain Theory and Gauss Theory) of analysis mechanics are expanded to apply to rigid system. For the unlinear and incomplete Constraint rigid system, by using Bertrand-Jourdain Theory, Wittenburg equation is expanded. The kinematic equation of the second-order unlinear and uncomplete constraint rigid system is inferred by applying Guass Theory.