一类广义Birkhoff系统的无限小正则变换与积分

葛伟宽; 张毅; 楼智美

doi:10.7498/aps.61.140204

摘要

研究一类广义Birkhoff系统的无限小正则变换与积分, 建立这类广义Birkhoff系统的方程,将Birkhoff系统的无限小正则变换与积分的有关结果推广到这类广义Birkhoff系统,举例说明结果的应用.

关键词:

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.

Keywords:

Birkhoff system /
generalized Birkhoff system /
infinitesimal canonical transformation /
integral

作者及机构信息

1.
湖州师范学院物理系, 湖州 313000;

2.
苏州科技学院土木工程学院, 苏州 215011;

3.
绍兴文理学院物理系, 绍兴 312000

基金项目: 国家自然科学基金(批准号: 10772025, 10932002)资助的课题.

Authors and contacts

1.
Department of Physics, Huzhou Teachers College, Huzhou 313000, China;

2.
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China;

3.
Department of Physics, Shaoxing University, Shaoxing 312000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10772025, 10932002).

参考文献

[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 物理学报 57 4649]
[8]	Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese) [梅凤翔, 蔡建乐 2008 物理学报 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 物理学报 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 物理学报 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)

施引文献

[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 物理学报 57 4649]
[8]	Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657 (in Chinese) [梅凤翔, 蔡建乐 2008 物理学报 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 物理学报 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 物理学报 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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