The discrete variational principle in Hamiltonian formalism and first integrals

doi:10.1088/1009-1963/14/6/001

中国物理B ›› 2005, Vol. 14 ›› Issue (6): 1063-1068.doi: 10.1088/1009-1963/14/6/001

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The discrete variational principle in Hamiltonian formalism and first integrals

张宏彬¹, 陈立群², 刘荣万²

(1)Department of Physics, Chaohu College, Chaohu 238000, China；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

收稿日期:2004-12-16 修回日期:2005-03-01 出版日期:2005-05-27 发布日期:2005-05-27
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.10172056) and the Science Research of the Education Bureau of Anhui Province (Grant No.2004KJ294)

The discrete variational principle in Hamiltonian formalism and first integrals

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

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

Received:2004-12-16 Revised:2005-03-01 Online:2005-05-27 Published:2005-05-27
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.10172056) and the Science Research of the Education Bureau of Anhui Province (Grant No.2004KJ294)

摘要/Abstract

摘要： The aim of this paper is to show that first integrals of discrete equation of motion for Hamiltonian systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian in phase space. The result obtained is a discrete analog of the theorem of Noether in the Calculus of variations.

关键词: discrete mechanics, Hamiltonian system, Noether’s theorem, first integral

Abstract: The aim of this paper is to show that first integrals of discrete equation of motion for Hamiltonian systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian in phase space. The result obtained is a discrete analog of the theorem of Noether in the Calculus of variations.

Key words: discrete mechanics, Hamiltonian system, Noether’s theorem, first integral

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

45.10.Db (Variational and optimization methods) 02.30.Xx (Calculus of variations) 02.30.Cj (Measure and integration)

张宏彬, 陈立群, 刘荣万. The discrete variational principle in Hamiltonian formalism and first integrals[J]. 中国物理B, 2005, 14(6): 1063-1068.

Zhang Hong-Bin (张宏彬), Chen Li-Qun (陈立群), Liu Rong-Wan (刘荣万). The discrete variational principle in Hamiltonian formalism and first integrals[J]. Chinese Physics, 2005, 14(6): 1063-1068.

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The discrete variational principle in Hamiltonian formalism and first integrals

The discrete variational principle in Hamiltonian formalism and first integrals

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