Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law

LONG Zixuan; ZHANG Yi

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Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law

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- Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 52, Issue 5, Pages: 51-56(2013)
- 作者机构：
  
  1. 苏州科技学院数理学院,江苏,苏州,215009
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2013，
  
  Published Online：25 October 2013，
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LONG Zixuan, ZHANG Yi. Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 52(5):51-56(2013)
DOI：

LONG Zixuan, ZHANG Yi. Noether's Theorem for Variational Problem Based on Fractional Integral Extended by Sine Periodic Law. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 52(5):51-56(2013) DOI：

摘要

基于按正弦周期律拓展的分数阶积分的类分数阶动力学建模方法，研究完整系统的类分数阶Noether对称性和守恒量。首先，基于按正弦周期律拓展的分数阶积分，建立了类分数阶变分问题，导出了类分数阶d'Alembert-Lagrange原理，给出了类分数阶Euler-Lagrange方程；其次，基于类分数阶Hamilton作用量在无限小群变换下的不变性，提出了类分数阶Noether对称变换和Noether准对称变换的定义和判据；最后，建立了类分数阶Noether定理，揭示了系统的Noether对称性与守恒量之间的关系，并举例说明结果的应用。

Abstract

Based on the fractional integral extended by sine periodic law introduced by EI-Nabulsi

the fractional action-like Noether symmetries and conserved quantities for holonomic systems are studied. First

the fractional actionlike variational problem based on the fractional integral extended by sine periodic law is established

the fractional action-like d'Alembert-Lagrange principle is deduced

as well as the fractional action-like Euler-Lagrange equations is obtained. Secondly

the definitions and criteria of the fractional actionlike Noether's (quasi-) symmetrical transformations are presented in terms of the invariance of the fractional action-like Hamilton action under the infinitesimal transformations of group. Finally

fractional action-like Noether's theorem for holonomic systems is explored

the relationship between the Noether symmetry and the conserved quantity of the system is revealed

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

关键词

类分数阶Noether定理按正弦周期律拓展的分数阶积分类分数阶（准）对称变换守恒量

Keywords

fractional action-like Noether theoremfractional integral extended by sine periodic lawfractional action-like (quasi-) symmetric transformationconserved quantity

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Related Author

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DING Jinfeng

ZHU Jianqing

HE Shengxin

ZHANG Yi

JIN Shixin

Related Institution

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



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

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

 2．苏州科技学院土木工程学院

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