北京大学学报（自然科学版） ›› 2016, Vol. 52 ›› Issue (4): 681-686.DOI: 10.13209/j.0479-8023.2016.080

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典型微扰力学系统的近似Lie对称性、近似Noether对称性和近似Mei对称性

楼智美1, 王元斌2, 谢志堃1   

  1. 1. 绍兴文理学院物理系, 绍兴 312000
    2. 绍兴文理学院数学系, 绍兴 312000
  • 收稿日期:2015-10-09 修回日期:2016-02-13 出版日期:2016-07-20 发布日期:2016-07-20
  • 通讯作者: 楼智美, E-mail: louzhimei(at)usx.edu.cn
  • 基金资助:
    国家自然科学基金(11472177)资助

Approximate Lie Symmetries, Approximate Noether Symmetries and Approximate Mei Symmetries of Typical Perturbed Mechanical System

LOU Zhimei1, WANG Yuanbin2, XIE Zhikun1   

  1. 1. Department of Physics, Shaoxing University, Shaoxing 312000
    2. Department of mathematics, Shaoxing University, Shaoxing 312000
  • Received:2015-10-09 Revised:2016-02-13 Online:2016-07-20 Published:2016-07-20
  • Contact: LOU Zhimei, E-mail: louzhimei(at)usx.edu.cn

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摘要：

利用3种近似对称性方法(近似Lie对称性法、近似Noether对称性法和近似Mei对称性法)研究典型微扰力学系统的一阶近似对称性和近似守恒量。结果表明, 利用近似Lie对称性法找到的6个一阶近似对称性和近似守恒量与利用近似Noether对称性法找到的相同, 而利用近似Mei对称性法只能找到其中5个一阶近似对称性和近似守恒量。

关键词: 微扰力学系统, 近似Lie对称性, 近似Noether对称性, 近似Mei对称性, 近似守恒量

Abstract:

Three methods, which are approximate Lie symmetry method, approximate Noether symmetry method and approximate Mei symmetry method, are adopted to study the first order approximate symmetries and approximate conserved quantities of a typical perturbed mechanical system. Six identical first order approximate symmetries and approximate conserved quantities of the typical perturbed mechanical system are obtained by approximate Lie symmetry method and approximate Noether symmetry method, but only five of them can be obtained by approximate Mei symmetry method.

Key words: perturbed mechanical system, approximate Lie symmetry, approximate Noether symmetry, approximate Mei symmetry, approximate conserved quantity

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