中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3139-3144.doi: 10.1088/1674-1056/18/8/007

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Conformal invariance and conserved quantities of dynamical system of relative motion

陈向炜, 赵永红, 李彦敏   

  1. Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China
  • 收稿日期:2009-02-27 修回日期:2009-03-09 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Henan Province, China (Grant Nos 082300410330 and 082300410370).

Conformal invariance and conserved quantities of dynamical system of relative motion

Chen Xiang-Wei(陈向炜)† , Zhao Yong-Hong(赵永红), and Li Yan-Min(李彦敏)   

  1. Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China
  • Received:2009-02-27 Revised:2009-03-09 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Henan Province, China (Grant Nos 082300410330 and 082300410370).

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摘要： This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Abstract: This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Key words: dynamical system of relative motion, infinitesimal transformation, conformal invariance, conserved quantities

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
02.20.Sv (Lie algebras of Lie groups) 45.10.Na (Geometrical and tensorial methods)