中国物理B ›› 2009, Vol. 18 ›› Issue (3): 856-860.doi: 10.1088/1674-1056/18/3/003

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Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

刘世兴1, 郭永新1, 刘畅2, 梅凤翔3   

  1. (1)College of Physics, Liaoning University, Shenyang 110036, China; (2)College of Physics, Liaoning University, Shenyang 110036, China;Department of Mechanics, Faculty of Science, Beijing Institute of Technology, Beijing 100081, China; (3)Department of Mechanics, Faculty of Science, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2007-12-24 修回日期:2008-06-06 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472040, 10572021 and 10772025) and the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005).

Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

Liu Chang(刘畅)a)b), Liu Shi-Xing(刘世兴)a), Mei Feng-Xiang(梅凤翔)b), and Guo Yong-Xin(郭永新)a)†   

  1. a College of Physics, Liaoning University, Shenyang 110036, China; b Department of Mechanics, Faculty of Science, Beijing Institute of Technology, Beijing 100081, China
  • Received:2007-12-24 Revised:2008-06-06 Online:2009-03-20 Published:2009-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10472040, 10572021 and 10772025) and the Outstanding Young Talents Training Found of Liaoning Province of China (Grant No 3040005).

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摘要： This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.

关键词: canonical Hamilton systems, infinitesimal transformations, conformal invariance, Hojman conserved quantities

Abstract: This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.

Key words: canonical Hamilton systems, infinitesimal transformations, conformal invariance, Hojman conserved quantities

中图分类号:  (General theory of classical mechanics of discrete systems)

  • 45.05.+x
02.30.Jr (Partial differential equations)