中国物理B ›› 2009, Vol. 18 ›› Issue (2): 395-399.doi: 10.1088/1674-1056/18/2/003

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Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

郭永新1, 刘畅2, 梅凤翔3   

  1. (1)College of Physics, Liaoning University, Shenyang 110036, China; (2)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (3)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2007-12-16 修回日期:2008-06-30 出版日期:2009-02-20 发布日期:2009-02-20
  • 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 conserved quantities of non-conservative Lagrange systems by point transformations

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

  1. a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b College of Physics, Liaoning University, Shenyang 110036, China
  • Received:2007-12-16 Revised:2008-06-30 Online:2009-02-20 Published:2009-02-20
  • 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 studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

关键词: non-conservative Lagrange systems, point transformations, conformal invariance, conserved quantities

Abstract: This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

Key words: non-conservative Lagrange systems, point transformations, conformal invariance, conserved quantities

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

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