Noether quasi-symmetry for non-conservative systems  based on fractional model

HE Shengxin; ZHU Jianqing; ZHANG Yi

doi:10.13471/j.cnki.acta.snus.2016.02.011

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Noether quasi-symmetry for non-conservative systems based on fractional model

更新时间：2023-12-11

- Noether quasi-symmetry for non-conservative systems based on fractional model
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 55, Issue 2, Pages: 58-63(2016)
- 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：10.13471/j.cnki.acta.snus.2016.02.011
  CLC：
- Published：2016，
  
  Published Online：25 March 2016，
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HE Shengxin, ZHU Jianqing, ZHANG Yi. Noether quasi-symmetry for non-conservative systems based on fractional model. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(2):58-63(2016)
DOI：

HE Shengxin, ZHU Jianqing, ZHANG Yi. Noether quasi-symmetry for non-conservative systems based on fractional model. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(2):58-63(2016) DOI： 10.13471/j.cnki.acta.snus.2016.02.011.

摘要

提出并研究了非保守力学系统的分数阶Noether对称性及其守恒量。基于非保守系统的Hamilton原理，导出了分数阶模型下非保守系统的运动微分方程；根据分数阶Hamilton作用量在时间，广义坐标和广义速度的无限小群变换下的不变性，给出了非保守力学系统的分数阶Noether准对称性的定义和判据，建立了分数阶Noether准对称性与守恒量之间的联系，得到了分数阶Noether守恒量；最后，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 Noether symmetries and conserved quantities for non-conservative systems are proposed and studied with fractional model. Based on the Hamilton principle for the non-conservative systems

the fractional differential equations of motion are derived. With using the invariance of the fractional Hamilton action under the infinitesimal transformations of group which depends on the time

the generalized coordinates and velocities

the definition and the criterion of the fractional Noether generalized quasi-symmetry for the non-conservative systems are given. The relation between the fractional Noether quasi-symmetry and the conserved quantity is established

and the fractional conserved quantities are obtained. The special cases

which the generalized nonpotential forces do 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

分数阶模型非保守系统Noether准对称性守恒量

Keywords

fractional modelnon-conservative systemNoether quasi-symmetryconserved quantity

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Related Author

ZHU Jianqing

HE Shengxin

LIU Yandong

ZHANG Yi

LONG Zixuan

ZHANG Yi

Related Institution

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

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



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

College of Civil Engineering, Suzhou University of Science and Technology

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