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Chin. Phys., 2004, Vol. 13(12): 1999-2002    DOI: 10.1088/1009-1963/13/12/004
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Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Mei Feng-Xianga, Qin Mao-Changa, Xu Xue-Junb
a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract  Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.
Keywords:  form invariance      non-Noether conserved quantity      Birkhoffian system  
Received:  11 May 2004      Revised:  03 June 2004      Published:  17 March 2005
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Hq (Ordinary differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10272021).

Cite this article: 

Mei Feng-Xiang, Qin Mao-Chang, Xu Xue-Jun Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system 2004 Chin. Phys. 13 1999

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