A class of quasi-fractional Noether‘’s theorems for nonconservative systems in event space

WANG Ze; ZHANG Yi

doi:10.13471/j.cnki.acta.snus.2019.06.015

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A class of quasi-fractional Noether‘’s theorems for nonconservative systems in event space

更新时间：2023-12-11

- A class of quasi-fractional Noether‘’s theorems for nonconservative systems in event space
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 58, Issue 6, Pages: 119-127(2019)
- 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：10.13471/j.cnki.acta.snus.2019.06.015
  CLC：
- Published：2019，
  
  Published Online：25 November 2019，
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WANG Ze, ZHANG Yi. A class of quasi-fractional Noether‘’s theorems for nonconservative systems in event space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(6):119-127(2019)
DOI：

WANG Ze, ZHANG Yi. A class of quasi-fractional Noether‘’s theorems for nonconservative systems in event space. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 58(6):119-127(2019) DOI： 10.13471/j.cnki.acta.snus.2019.06.015.

摘要

为了深入研究非保守动力学系统的对称性和守恒量，提出并研究事件空间中基于周期律拓展的拟分数阶模型的Noether定理。首先提出事件空间中基于按周期律拓展的分数阶积分的El-Nabulsi分数阶变分问题，求解出该模型下完整非保守系统与非完整非保守系统的运动微分方程；其次，基于作用量泛函在无限小变换下的不变性，建立Noether对称变换和Noether准对称变换的定义和判据；最后，提出并证明了事件空间中基于按周期律拓展的拟分数阶模型的Noether定理，并给出两个算例以说明定理的应用。

Abstract

To study the symmetry and conserved quantity of fractional non-conservative dynamic systems

the Noether theorem based on El-Nabulsi periodic law quasi-fractional model in event space is proposed and studied. Firstly

the fractional order variational problem based on the El-Nabulsi periodic law quasifractional model is established in the event space

and the differential equations of the holonomic nonconservative system and the nonholonomic nonconservative system are derived. Secondly

based on the invariance of the action functional under the infinitesimal transformation

the definition and criterion of the Noether symmetric transform and the Noether quasi-symmetric transformation are given. Finally

the Noether theorem based on the El-Nabulsi periodic law quasifractional model in the event space is proposed and proved. Two examples are given to illustrate the application of the results.

关键词

事件空间Noether定理拟分数阶模型按周期律拓展的分数阶积分

Keywords

event spaceNoethers theoremquasi-fractional modelfractional integral extended by periodic laws

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