Form invariances and Lutzky conserved quantities for Lagrange systems
Mei Feng-Xiang (梅凤翔)a, Xu Xue-Jun (许学军)ab
a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result.
Received: 13 September 2004
Revised: 12 October 2004
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
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