The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

doi:10.1088/1674-1056/17/2/005

中国物理B ›› 2008, Vol. 17 ›› Issue (2): 385-389.doi: 10.1088/1674-1056/17/2/005

The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

傅景礼¹, 陈立群², 施沈阳³

(1)Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (3)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2006-07-14 修回日期:2007-05-11 出版日期:2008-02-20 发布日期:2008-02-20
基金资助:
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).

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)

^a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; ^b Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2006-07-14 Revised:2007-05-11 Online:2008-02-20 Published:2008-02-20
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: discrete mechanics, total variational principle, Lie symmetry, discrete conserved quantity

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.

Key words: discrete mechanics, total variational principle, Lie symmetry, discrete conserved quantity

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

45.05.+x

45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.30.Jr (Partial differential equations) 02.20.Qs (General properties, structure, and representation of Lie groups)

施沈阳, 傅景礼, 陈立群. The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems[J]. 中国物理B, 2008, 17(2): 385-389.

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[J]. Chin. Phys. B, 2008, 17(2): 385-389.

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The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems

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