The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems
Shi Shen-Yang(施沈阳)a) b) †, Fu Jing-Li(傅景礼)b), and Chen Li-Qun(陈立群)a)
aShanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; b Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.
Received: 14 July 2006
Revised: 11 May 2007
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
(General properties, structure, and representation of Lie groups)
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10672143) and the
Natural Science Foundation of Henan Province, China (Grant No
0511022200).
Cite this article:
Shi Shen-Yang(施沈阳), Fu Jing-Li(傅景礼), and Chen Li-Qun(陈立群) The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems 2008 Chin. Phys. B 17 385
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