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
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.
Received: 30 March 2006
Revised: 29 May 2006
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: 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).
Cite this article:
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 2007 Chinese Physics 16 582
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
