关于力学系统的守恒律

On Conservation Laws of Mechanical Systems

摘要: 守恒律在数学、力学和物理学中是非常有效的工具. 介绍寻求守恒律的 3种方法. 首先, 概述牛顿力学方法及其近代发展. 其次, 介绍 L agrange力学方法及其发展. 最后, 研究对称性方法, 主要是 Noether对称性、L ie对称性和形式不变性方法.

Abstract: Conservation laws are extremely useful tools in mathematics, mechanics and physics. Three methods in arriving at the conservation laws are presented in this work. The method of Newtonian mechanics and its modern developments are first sammarised. Method of Lagrange mechanics and its developments are then presented, followed by the symmetry methods.