Abstract:

Analytical mechanics is established based on d’Almbert-Lagrange Principle, Gauss principle, Jourdian principle and Hamilton principle, to deal with the dynamics of mechanical systems subject to holonomic or nonholonomic constraints. The governing equation of the systems are derived either by introducing Lagrange’s multipliers to adjoin with the limitation equations for the virtual displacements, or by directly eliminating the constraint equations to achieve minimal formulations. The author presents a survey for the history of analytical mechanics, and explains some basic concepts, such as virtual displacement, ideal constraint, and the correlations between the Lagrange multipliers and the real constraint forces.

Key words: nonholonomic constraints, basic principles, virtual displacements, ideal constraints

摘要：

对于受约束的系统, 分析动力学主要基于 d’Almbert-Lagrange 原理、Gauss 原理、Jourdian 原理和Hamilton 原理等, 利用虚位移限制方程, 建立包含乘子的动力学基本方程, 或利用约束嵌入的方式, 降低系统动力学方程的维数。作者系统回顾分析动力学发展历程, 对一些基本概念, 如虚位移、理想约束、Lagrange 乘子与约束力之间的关系等, 给出诠释。

关键词: 非完整约束, 力学基本原理, 虚位移, 理想约束