Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians

SONG Jing; ZHANG Yi

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Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians

更新时间：2023-12-11

- Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 56, Issue 3, Pages: 26-30(2017)
- 作者机构：
  
  1. 苏州科技大学数理学院,江苏,苏州,215009
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2017，
  
  Published Online：25 May 2017，
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SONG Jing, ZHANG Yi. Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 56(3):26-30(2017)
DOI：

SONG Jing, ZHANG Yi. Noether-Mei symmetry and conserved quantity for dynamical systems with non-standard Lagrangians. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 56(3):26-30(2017) DOI：

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。

Abstract

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.

关键词

非标准Lagrange函数NoetherMei对称性Noether守恒量Mei守恒量

Keywords

non-standrad LagrangianNoether-Mei symmetryNoether conserved quantityMei conserved quantity

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Related Author

WANG Xueping

ZHANG Yi

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苏州科技大学数理学院，江苏苏州215009 苏州科技大学土木工程学院

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