中国物理B ›› 2008, Vol. 17 ›› Issue (9): 3170-3174.doi: 10.1088/1674-1056/17/9/002

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Conformal invariance and conserved quantity of Hamilton systems

梅凤翔1, 蔡建乐2, 罗绍凯3   

  1. (1)College of Science, Beijing Institute of Technology, Beijing 100081, China; (2)College of Science, Hangzhou Normal University, Hangzhou 310018, China;College of Science, Beijing Institute of Technology, Beijing 100081, China; (3)Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
  • 收稿日期:2007-12-25 修回日期:2008-01-24 出版日期:2008-09-08 发布日期:2008-09-08
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).

Conformal invariance and conserved quantity of Hamilton systems

Cai Jian-Le(蔡建乐)a)c)†, Luo Shao-Kai(罗绍凯)b), and Mei Feng-Xiang(梅凤翔)c)   

  1. a College of Science, Hangzhou Normal University, Hangzhou 310018, China; b Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; c College of Science, Beijing Institute of Technology, Beijing 100081, China
  • Received:2007-12-25 Revised:2008-01-24 Online:2008-09-08 Published:2008-09-08
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).

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摘要： This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.

关键词: Hamilton system, conformal invariance, determining equation, conserved quantity

Abstract: This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.

Key words: Hamilton system, conformal invariance, determining equation, conserved quantity

中图分类号:  (Celestial mechanics)

  • 45.50.Pk
02.30.Jr (Partial differential equations) 45.20.Jj (Lagrangian and Hamiltonian mechanics)