Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations
Fu Jing-Li (傅景礼)ac, Chen Li-Qun (陈立群)bc, Xie Feng-Ping (谢凤萍)a
a Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; b Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; c 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.
Received: 02 December 2003
Revised: 10 March 2004
Accepted manuscript online:
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 (傅景礼), Chen Li-Qun (陈立群), Xie Feng-Ping (谢凤萍) Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations 2004 Chinese Physics 13 1611
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