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The discrete variational principle and the first integrals of Birkhoff systems* 被引量:5

The discrete variational principle and the first integrals of Birkhoff systems*
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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. 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.
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第3期582-587,共6页 中国物理B(英文版)
基金 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). Acknowledgement We wish to thank the referees for their careful reading of the manuscript and their useful remarks which helped us to improve the quality of this paper.
关键词 discrete mechanics Birkhoff system discrete Pfaffian Noether's theorem first integral discrete mechanics, Birkhoff system, discrete Pfaffian, Noether's theorem, first integral
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参考文献18

  • 1Birkhoff G D 1927 Dynamical Systems (Providence RI:AMS College Publications)
  • 2Santilli R M 1978 Foundations of Theoretical MechanicsI (New York: Springer)
  • 3Santilli R M 1983 Foundations of Theoretical Mechanics II (New York: Springer)
  • 4Mei F X, Shi R C, Zhang Y F and Wu H B 1996 Dynamics of Birkhoff System (Beijing: Beijing Institute of Technology Press) (in Chinese)
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  • 10Fu J L and Wang X M 2000 Acta Phys. Sin. 49 1023 (in Chinese)

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