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.
Received: 15 February 2009
Revised: 10 March 2009
Accepted manuscript online:
(General properties, structure, and representation of Lie groups)
Fund: Project supported by the Graduate
Students Innovative Foundation of China University of Petroleum
(East China) (Grant No S2009-19).
Cite this article:
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) Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems 2009 Chin. Phys. B 18 4650
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