基于非标准Lagrange函数的动力学系统的Noether-Mei对称性与守恒量

摘要

研究基于两类非标准Lagrange函数(指数Lagrange函数和Lagrange幂函数)的动力学系统的Noether-Mei对称性及其守恒量.首先,给出基于指数Lagrange函数和Lagrange幂函数的动力学系统的Noether-Mei对称性的定义与判据;其次,提出由系统的Noether-Mei对称性导致的Noether守恒量与Mei守恒量的存在条件及其形式,给出四个Noether-Mei对称性定理.最后,举例说明结果的应用.%This paper focuses on studying the Noether-Mei symmetry and the conserved quantity for dynamical systems with non-standard Lagrangians (exponential Lagrangians and power law Lagrangians).Firstly,The definition and the criteria of Noether-Mei symmetry for dynamical systems with non-standard Lagrangians are given.Secondly,The conditions that Noether-Mei symmetry leads to Noether conserved quantity or Mei conserved quantity and the form of conserved quantities are put forward.And four theorems for Noether-Mei symmetry and conserved quantities are established.Two examples are given to illustrate the application of the results.