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An infinitesimal canonical transformation and an integral for a generalized Birkhoff system are studied. The equations of the generalized Birkhoff system are established. The results of the infinitesimal canonical transformation and the integral for the Birkhoff system are generalized to the generalized Birkhoff system. An example is given to illustrate the application of the result.
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Keywords:
- Birkhoff system /
- generalized Birkhoff system /
- infinitesimal canonical transformation /
- integral
[1] Wittaker E T 1937 A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (4th Ed.) (Cambridge: Cambridge Univ. Press)
[2] Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York: Springer-Verlag)
[3] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔, 史荣昌, 张永发, 吴惠彬 1996 Birkhoff系统动力学 (北京: 北京理工大学出版社)]
[4] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: RZUFN) (in Russian)
[5] Mei F X 1993 Sience in China Ser A 36 1456
[6] Mei F X, Zhang Y F, He G, Gang T Q, Xie J F 2007 J. Beijing Institute of Technology 27 1035 (in Chinese) [梅凤翔, 张永发, 何光, 冮铁强, 解加芳 2007 北京理工大学学报 27 1035]
[7] Mei F X, Xie J F, Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese) [梅凤翔, 解加芳, 冮铁强 2008 57 4649]
[8] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese) [梅凤翔, 蔡建乐 2008 57 4657]
[9] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583
[10] Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699 (in Chinese) [葛伟宽, 梅凤翔 2009 58 699]
[11] Shang M, Mei F X 2009 Chin. Phys. B 18 3155
[12] Li Y M, Mei F X 2010 Chin. Phys. B 19 080302
[13] Ge W K, Zhang Y 2011 Acta Phys. Sin. 60 050202 (in Chinese) [葛伟宽, 张毅 2011 60 050202]
[14] Mei F X, Chui J C 2011 J. Beijing Institute of Technology 20 285
[15] Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V) (in Russian)
[16] Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical System (Beijing: Beijing Institute of Technology Press)
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[1] Wittaker E T 1937 A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (4th Ed.) (Cambridge: Cambridge Univ. Press)
[2] Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York: Springer-Verlag)
[3] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoffian System (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔, 史荣昌, 张永发, 吴惠彬 1996 Birkhoff系统动力学 (北京: 北京理工大学出版社)]
[4] Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow: RZUFN) (in Russian)
[5] Mei F X 1993 Sience in China Ser A 36 1456
[6] Mei F X, Zhang Y F, He G, Gang T Q, Xie J F 2007 J. Beijing Institute of Technology 27 1035 (in Chinese) [梅凤翔, 张永发, 何光, 冮铁强, 解加芳 2007 北京理工大学学报 27 1035]
[7] Mei F X, Xie J F, Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese) [梅凤翔, 解加芳, 冮铁强 2008 57 4649]
[8] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese) [梅凤翔, 蔡建乐 2008 57 4657]
[9] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583
[10] Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699 (in Chinese) [葛伟宽, 梅凤翔 2009 58 699]
[11] Shang M, Mei F X 2009 Chin. Phys. B 18 3155
[12] Li Y M, Mei F X 2010 Chin. Phys. B 19 080302
[13] Ge W K, Zhang Y 2011 Acta Phys. Sin. 60 050202 (in Chinese) [葛伟宽, 张毅 2011 60 050202]
[14] Mei F X, Chui J C 2011 J. Beijing Institute of Technology 20 285
[15] Novoselov V S 1966 Variational Methods in Mechanics (Leningrad: L G V) (in Russian)
[16] Mei F X, Wu H B 2009 Dynamics of Constrained Mechanical System (Beijing: Beijing Institute of Technology Press)
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