Noether Quasi-Symmetry for Nonconservative Mechanical System in Phase Space Based on Fractional Models

HE Shengxin; ZHU Jianqing

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Noether Quasi-Symmetry for Nonconservative Mechanical System in Phase Space Based on Fractional Models

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- Noether Quasi-Symmetry for Nonconservative Mechanical System in Phase Space Based on Fractional Models
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 54, Issue 4, Pages: 37-42(2015)
- 作者机构：
  
  苏州科技学院数理学院,江苏,苏州,215009
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2015，
  
  Published Online：25 August 2015，
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HE Shengxin, ZHU Jianqing. Noether Quasi-Symmetry for Nonconservative Mechanical System in Phase Space Based on Fractional Models. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(4):37-42(2015)
DOI：

HE Shengxin, ZHU Jianqing. Noether Quasi-Symmetry for Nonconservative Mechanical System in Phase Space Based on Fractional Models. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 54(4):37-42(2015) DOI：

摘要

提出并讨论了相空间中非保守力学系统的分数阶Noether对称性与守恒量。给出非保守Hamilton系统的分数阶Hamilton原理，建立了分数阶Hamilton正则方程；依据分数阶Hamilton作用量在无限小群变换下的不变性，得到了非保守相空间中分数阶Noether准对称变换的定义和判据，建立了非保守相空间中分数阶Noether准对称性与守恒量之间的联系，得到了相空间中分数阶守恒量；讨论了不存在非势广义力或规范函数等于零的特例，并举例说明结果的应用。

Abstract

The fractional Noether symmetries and fractional conserved quantities for a non-conservative system in phase space are proposed and discussed. Firstly

the fractional Hamilton canonical equations for the non-conservative system are established. Secondly

based upon the invariance of the fractional Hamilton action under the infinitesimal transformations of group

the definitions and criterion of fractional Noether quasi-symmetric transformations are obtained

then the relationship between a fractional Noether symmetry and a fractional conserved quantity of nonconservative system in phase space is established

and the fractional conserved quantity is obtained. Finally

the special cases

which the generalized nonpotential forces are not exit or the gauge function is equal to zero

are discussed. At the end

two examples are given to illustrate the application of the results.

关键词

分数阶模型相空间Noether准对称性守恒量

Keywords

fractional modelphase spaceNoether quasi-symmetryconserved quantity

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Related Author

ZHANG Yi

ZHU Jianqing

HE Shengxin

ZHANG Yi

JIN Shixin

LIU Yandong

ZHANG Yi

Related Institution

 2．苏州科技学院土木工程学院

 苏州科技学院数理学院

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

．苏州科技学院数理学院

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

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