The discrete variational principle and the first integrals of Birkhoff systems

doi:10.1088/1009-1963/16/3/004

中国物理B ›› 2007, Vol. 16 ›› Issue (3): 582-587.doi: 10.1088/1009-1963/16/3/004

The discrete variational principle and the first integrals of Birkhoff systems

顾书龙¹, 柳传长¹, 张宏彬², 陈立群³

(1)Department of Physics, Chaohu College, Chaohu 238000, China; (2)Department of Physics, Chaohu College, Chaohu 238000, China;Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (3)Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Department of Mechanics, Shanghai University, Shanghai 200436, China

收稿日期:2006-03-30 修回日期:2006-05-29 出版日期:2007-03-20 发布日期:2007-03-20
基金资助:
Project partially supported by the National Natural Science Foundation of China (Grant No~10172056) and the Science Research of the Education Bureau of Anhui Province, China (Grant No~2006KJ263B).

The discrete variational principle and the first integrals of Birkhoff systems

Zhang Hong-Bin(张宏彬)^a)b)†, Chen Li-Qun(陈立群)^b)c), Gu Shu-Long(顾书龙)^a), and Liu Chuan-Zhang(柳传长)^a)

^a Department of Physics, Chaohu College, Chaohu 238000, China; ^b Shanghai Institute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; ^c Department of Mechanics, Shanghai University, Shanghai 200436, China

Received:2006-03-30 Revised:2006-05-29 Online:2007-03-20 Published:2007-03-20
Supported by:
Project partially supported by the National Natural Science Foundation of China (Grant No~10172056) and the Science Research of the Education Bureau of Anhui Province, China (Grant No~2006KJ263B).

摘要/Abstract

摘要： This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.

关键词: discrete mechanics, Birkhoff system, discrete Pfaffian, Noether's theorem, first integral

Abstract: This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.

Key words: discrete mechanics, Birkhoff system, discrete Pfaffian, Noether's theorem, first integral

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

45.05.+x

02.30.Ik (Integrable systems) 02.30.Jr (Partial differential equations)

张宏彬, 陈立群, 顾书龙, 柳传长. The discrete variational principle and the first integrals of Birkhoff systems[J]. 中国物理B, 2007, 16(3): 582-587.

Zhang Hong-Bin(张宏彬), Chen Li-Qun(陈立群), Gu Shu-Long(顾书龙), and Liu Chuan-Zhang(柳传长). The discrete variational principle and the first integrals of Birkhoff systems[J]. Chinese Physics, 2007, 16(3): 582-587.

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The discrete variational principle and the first integrals of Birkhoff systems

The discrete variational principle and the first integrals of Birkhoff systems

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