Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space

JIN Shixin; ZHANG Yi

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Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space

更新时间：2023-12-11

- Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 4, Pages: 56-61(2014)
- 作者机构：
  
  1. ．苏州科技学院数理学院,江苏,苏州,215009
  2.  2．苏州科技学院土木工程学院,江苏,苏州,215009
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 July 2014，
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JIN Shixin, ZHANG Yi. Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(4):56-61(2014)
DOI：

JIN Shixin, ZHANG Yi. Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(4):56-61(2014) DOI：

摘要

研究相空间中含时滞的非保守力学系统的Noether对称性与守恒量。建立含时滞的非保守系统动力学的Hamilton正则方程；依据相空间中含时滞的Hamilton作用量在无限小群变换下的广义准不变性，给出相空间中含时滞的Noether广义准对称变换的定义和判据；并建立相空间中含时滞的非保守力学系统的Noether对称性与守恒量之间的联系。文末，举例说明结果的应用。

Abstract

The Noether symmetries and the conserved quantities for nonconservative mechanical systems with time delay in phase space are studied. Firstly

the Hamilton canonical equations with time delays for the non-conservative systems are established. Secondly

according to the generalized quasi-invariance of the Hamilton action with time delay in phase space under the infinitesimal transformations of groups

the definitions and criterion of the Noether generalized quasisymmetric transformations with time delay in phase space are given. Lastly

the relationship between the Noether symmetries and the conserved quantities with time delay in phase space are established. At the end

an example is given to illustrate the application of the results.

关键词

非保守系统Noether对称性时滞相空间守恒量

Keywords

nonconservative systemNoether generalized quasisymmetrytime delayphase spaceconserved quantity

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Related Author

JIN Shixin

ZHANG Yi

ZHU Jianqing

HE Shengxin

DING Jinfeng

ZHANG Yi

JIN Shixin

JI Xiaohui

Related Institution

．南京理工大学理学院

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou

College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou

 3．苏州科技大学土木工程学院

 2．南京理工大学理学院

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