中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4650-4656.doi: 10.1088/1674-1056/18/11/007

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Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

张明江, 方建会, 路凯, 张克军, 李燕   

  1. College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
  • 收稿日期:2009-02-15 修回日期:2009-03-10 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:
    Project supported by the Graduate Students Innovative Foundation of China University of Petroleum (East China) (Grant No S2009-19).

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

Zhang Ming-Jiang(张明江), Fang Jian-Hui(方建会)†, Lu Kai(路凯), Zhang Ke-Jun(张克军), and Li Yan(李燕)   

  1. College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
  • Received:2009-02-15 Revised:2009-03-10 Online:2009-11-20 Published:2009-11-20
  • Supported by:
    Project supported by the Graduate Students Innovative Foundation of China University of Petroleum (East China) (Grant No S2009-19).

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摘要： This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

Abstract: This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.

Key words: conformal invariance, conserved quantity, third-order Lagrange equation, non-conserved mechanical system

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.05.+x (General theory of classical mechanics of discrete systems) 02.20.Qs (General properties, structure, and representation of Lie groups)