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Chin. Phys., 2004, Vol. 13(10): 1611-1614    DOI: 10.1088/1009-1963/13/10/005
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Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations

Xie Feng-Pinga, Fu Jing-Lib, Chen Li-Qunc
a Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; b Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; c Department of Mechanics, Shanghai University, Shanghai 200072, China; Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
Abstract  This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.
Keywords:  Lie groups      Hamiltonian system      Lie symmetry      non-Noether conserved quantity  
Received:  02 December 2003      Revised:  10 March 2004      Published:  20 June 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 10372053) and National Science Foundation of Henan Province, China (Grant No 0311011400).

Cite this article: 

Fu Jing-Li, Chen Li-Qun, Xie Feng-Ping Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations 2004 Chin. Phys. 13 1611

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