中国物理B ›› 2006, Vol. 15 ›› Issue (1): 19-21.doi: 10.1088/1009-1963/15/1/004

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Lie symmetry and conserved quantity of a system of first-order differential equations

梅凤翔1, 张永发1, 许学军2   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology,Beijing 100081, China; (2)Department of Mechanics, Beijing Institute of Technology,Beijing 100081, China;Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2005-04-22 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).

Lie symmetry and conserved quantity of a system of first-order differential equations

Xu Xue-Jun (许学军)ab, Mei Feng-Xiang (梅凤翔)a, Zhang Yong-Fa (张永发)a   

  1. a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2005-04-22 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).

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摘要： This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.

关键词: Lie symmetry, conserved quantity, differential equation, mechanical system

Abstract: This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.

Key words: Lie symmetry, conserved quantity, differential equation, mechanical system

中图分类号:  (Ordinary differential equations)

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