The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass
Shi Shen-Yang(施沈阳)a)b)†, Fu Jing-Li(傅景礼)a), Huang Xiao-Hong(黄晓虹)c),Chen Li-Qun(陈立群)b), and Zhang Xiao-Bo(张晓波)a)
a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; bShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; c School of Physics and Electronic Information, Wenzhou University, Wenzhou 325000, China
Abstract This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler--Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.
Received: 21 May 2007
Revised: 01 August 2007
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: Project supported by the National
Natural Science Foundation of
China (Grant No 10672143).
Cite this article:
Shi Shen-Yang(施沈阳), Fu Jing-Li(傅景礼), Huang Xiao-Hong(黄晓虹), Chen Li-Qun(陈立群), and Zhang Xiao-Bo(张晓波) The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass 2008 Chin. Phys. B 17 754
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