Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates
Shi Shen-Yang(施沈阳)a)† and Huang Xiao-Hong(黄晓虹)b)
a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b School of Physics and Electronic Information, Wenzhou University, Wenzhou 325000, China
Abstract The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.
Received: 31 July 2007
Revised: 12 September 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) and Huang Xiao-Hong(黄晓虹) Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates 2008 Chin. Phys. B 17 1554
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