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Chin. Phys. B, 2011, Vol. 20(5): 054501    DOI: 10.1088/1674-1056/20/5/054501

Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system

Zhang Ke-Jun, Fang Jian-Hui, Li Yan
College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
Abstract  Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant induced from the Mei symmetry of the system without perturbation is given. The criterion of the perturbation to Mei symmetry is established and the discrete Mei adiabatic invariant induced from the perturbation to Mei symmetry is obtained. Meanwhile, an example is discussed to illustrate the application of the results.
Keywords:  Mei adiabatic invariant      discrete generalized Birkhoffian system      Mei symmetry      perturbation     
Received:  13 September 2010      Published:  15 May 2011
PACS:  45.05.+x (General theory of classical mechanics of discrete systems)  
  02.20.Sv (Lie algebras of Lie groups)  
Fund: Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 09CX04018A).

Cite this article: 

Zhang Ke-Jun, Fang Jian-Hui, Li Yan Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system 2011 Chin. Phys. B 20 054501

[1] Zhao Y Y and Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) (in Chinese)
[2] Birkhoff G D 1927 Dynamical Systems (Providence RI: AMS College Publications)
[3] Santilli R M 1978 Foundations of Theoretical Mechanics (New York: Springer)
[4] Mei F X 1993 Sci. China Ser. A 36 1456
[5] Chen X W, Luo S K and Mei F X 2000 Acta Mech. Sol. Sin. 21 251 (in Chinese)
[6] Guo H Y, Luo S K and Mei F X 2001 Rep. Math. Phys. 47 33
[7] Fu J L, Chen L Q, Luo Y and Luo S K 2003 Chin. Phys. 12 351
[8] Luo S K and Cai J L 2003 Chin. Phys. 12 357
[9] Zhang Y 2004 Commun. Theor. Phys. 42 669
[10] Gu S L and Zhang H B 2004 Chin. Phys. 13 979
[11] Xu X J, Mei F X and Qin M C 2004 Chin. Phys. 13 1999
[12] Xu Z X 2005 Acta Phys. Sin. 54 4971 (in Chinese)
[13] Qiao Y F, Zhao S H and Li R J 2006 Chin. Phys. 15 2777
[14] Zhang P Y and Fang J H 2006 Acta Phys. Sin. 55 3813 (in Chinese)
[15] Chen X W, Zhang R C and Mei F X 2000 Acta Mech. Sin. 16 282
[16] Zhang Y 2002 Acta Phys. Sin. 51 1666 (in Chinese)
[17] Fu J L, Chen L Q and Xie F P 2003 Acta Phys. Sin. 52 2664 (in Chinese)
[18] Fu J L and Chen L Q 2004 Phys. Lett. A 324 95
[19] Luo S K and Guo Y X 2007 Commun. Theor. Phys. 47 25
[20] Ding N and Fang J H 2008 Commun. Theor. Phys. 49 1410
[21] Ding N, Fang J H and Chen X X 2008 Chin. Phys. B 17 1967
[22] Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 1
[23] Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 129
[24] Guo H Y, Li Y Q, Wu K and Wang S K 2002 Commun. Theor. Phys. 37 257
[25] Guo H Y and Wu K 2003 J. Math. Phys. 44 5978
[26] Luo X D, Guo H Y, Li Y Q and Wu K 2004 Commun. Theor. Phys. 42 443
[27] Zhang K J, Fang J H and Li Y 2010 Chin. Phys. B 19 124601 endfootnotesize
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