First integrals of the discrete nonconservative and nonholonomic systems

doi:10.1088/1009-1963/14/2/003

中国物理B ›› 2005, Vol. 14 ›› Issue (2): 238-243.doi: 10.1088/1009-1963/14/2/003

First integrals of the discrete nonconservative and nonholonomic systems

陈立群¹, 刘荣万¹, 张宏彬²

(1)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Physics, Chaohu University, Chaohu 238000, China

收稿日期:2004-06-14 修回日期:2004-09-24 出版日期:2005-03-02 发布日期:2005-03-02
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10172056) and Science Research Foundation of the Education Bureau of Anhui Province, China (Grant No 2004kj 294).

First integrals of the discrete nonconservative and nonholonomic systems

Zhang Hong-Bin (张宏彬)^ab, Chen Li-Qun (陈立群)^a, Liu Rong-Wan (刘荣万)^a

^a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; ^b Department of Physics, Chaohu University, Chaohu 238000, China

Received:2004-06-14 Revised:2004-09-24 Online:2005-03-02 Published:2005-03-02
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10172056) and Science Research Foundation of the Education Bureau of Anhui Province, China (Grant No 2004kj 294).

摘要/Abstract

摘要： In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations.

关键词: discrete mechanics, nonconservative and nonholonomic mechanical systems, Noether's theorem, first integral

Abstract: In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations.

Key words: discrete mechanics, nonconservative and nonholonomic mechanical systems, Noether's theorem, first integral

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

45.05.+x

45.20.Jj (Lagrangian and Hamiltonian mechanics) 45.10.Db (Variational and optimization methods) 02.30.Rz (Integral equations)

张宏彬, 陈立群, 刘荣万. First integrals of the discrete nonconservative and nonholonomic systems[J]. 中国物理B, 2005, 14(2): 238-243.

Zhang Hong-Bin (张宏彬), Chen Li-Qun (陈立群), Liu Rong-Wan (刘荣万). First integrals of the discrete nonconservative and nonholonomic systems[J]. Chinese Physics, 2005, 14(2): 238-243.

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First integrals of the discrete nonconservative and nonholonomic systems

First integrals of the discrete nonconservative and nonholonomic systems

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