Noether symmetry and Lie symmetry of discrete  holonomic systems with dependent coordinates

doi:10.1088/1674-1056/17/5/004

中国物理B ›› 2008, Vol. 17 ›› Issue (5): 1554-1559.doi: 10.1088/1674-1056/17/5/004

Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

施沈阳¹, 黄晓虹²

(1)Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (2)School of Physics and Electronic Information, Wenzhou University, Wenzhou 325000, China

收稿日期:2007-07-31 修回日期:2007-09-12 出版日期:2008-05-20 发布日期:2008-05-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10672143).

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

Received:2007-07-31 Revised:2007-09-12 Online:2008-05-20 Published:2008-05-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10672143).

摘要/Abstract

摘要： 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.

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.

Key words: discrete mechanics, Noether symmetry, Lie symmetry, discrete conserved quantity

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.30.Jr (Partial differential equations)

施沈阳, 黄晓虹. Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates[J]. 中国物理B, 2008, 17(5): 1554-1559.

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[J]. Chin. Phys. B, 2008, 17(5): 1554-1559.

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Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates

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