中国物理B ›› 2007, Vol. 16 ›› Issue (3): 599-604.doi: 10.1088/1009-1963/16/3/007

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A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

傅景礼1, 刘鸿基2, 唐贻发3   

  1. (1)Department of Physics, Zhejiang Sci-Tech University,Hangzhou 310018, China;State Key Laboratory of Scientific and Engineering Computing, ICMSEC,Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China; (2)Institute of Mathematical Physics, Shangqiu Teacher's College, Shangqiu 476000, China; (3)State Key Laboratory of Scientific and Engineering Computing, ICMSEC,Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2005-06-14 修回日期:2006-07-20 出版日期:2007-03-20 发布日期:2007-03-20
  • 基金资助:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos 10672143, 10471145 and 10372053) and the Natural Science Foundation of Henan Province Government of China(Grant Nos 0511022200 and 0311011400).

A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

Liu Hong-Ji(刘鸿基)a), Fu Jing-Li(傅景礼)b)d)†, and Tang Yi-Fa(唐贻发)c)   

  1. a Institute of Mathematical Physics, Shangqiu Teacher's College, Shangqiu 476000, China; b Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; c State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China; d Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • Received:2005-06-14 Revised:2006-07-20 Online:2007-03-20 Published:2007-03-20
  • Supported by:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos 10672143, 10471145 and 10372053) and the Natural Science Foundation of Henan Province Government of China(Grant Nos 0511022200 and 0311011400).

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摘要： In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

关键词: Mei symmetry, non-Noether conservative quantity, Lutzky conservative quantity, nonconservative system

Abstract: In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

Key words: Mei symmetry, non-Noether conservative quantity, Lutzky conservative quantity, nonconservative system

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.05.+x (General theory of classical mechanics of discrete systems)