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一类广义Birkhoff系统的广义正则变换

李彦敏 梅凤翔

一类广义Birkhoff系统的广义正则变换

李彦敏, 梅凤翔
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  • 研究一类广义Birkhoff系统的广义正则变换. 建立这类广义Birkhoff系统的运动微分方程, 得到了该系统的广义正则变换以及保持广义正则变换的条件. 最后, 举例说明结果的应用.
    • 基金项目: 国家自然科学基金(批准号: 10772025, 10932002, 10972127),河南省自然科学基金(批准号: 082300410330,082300410370,102300410144)资助的课题.
    [1]

    Santilli R M 1978 Foundations of theoretical mechanicsⅠ(New York: Springer Verlag)

    [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 Birkhoff Systems (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]

    Zhang H B 2001 Acta Phys. Sin. 50 1837(in Chinese)[张宏彬 2001 物理学报 50 1837]

    [5]

    Guo Y X, Luo S K, Shang M 2001 Rep. Math. Phys. 47 313

    [6]

    Luo S K, Lu Y B, Zhou Q, Wang Y D, Ou Y S 2002 Acta Phys. Sin. 51 1913(in Chinese)[罗绍凯、卢一兵、周 强、王应德、欧阳实2002 物理学报 51 1913]

    [7]

    Shang M, Guo Y X, Mei F X 2007 Chin. Phys. 16 292

    [8]

    Ge W K, Mei F X 2007 Acta Phys. Sin. 56 2476(in Chinese)[葛伟宽、梅凤翔2007 物理学报 56 2479]

    [9]

    Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678

    [10]

    Fu J L, Chen L Q, Luo S K, Chen X W, Wang X M 2001 Acta Phys. Sin. 50 2289(in Chinese)[傅景礼、陈立群、罗绍凯、陈向炜、王新民 2001 物理学报 50 2289]

    [11]

    Zhang Y 2008 Acta Phys. Sin. 57 5374(in Chinese)[张 毅2008 物理学报 57 5374]

    [12]

    Gu S L, Zhang H B 2004 Chin. Phys. 13 979

    [13]

    Ding N, Fang J H, Chen X X 2008 Chin. Phys. B 17 1967

    [14]

    Chen X W, Zhang R C, Mei F X 2000 Acta Mech. Sin. 16 282

    [15]

    Chen X W, Mei F X 2000 Mechanics Research Communications 27 365

    [16]

    Chen X W 2002 Chin. Phys. 11 441

    [17]

    Li Y M 2008 J. of Henan Normal University 36 52[李彦敏2008河南师范大学学报(自然科学版) 36 52]

    [18]

    Wang P, Fang J H, Wang X M 2009 Chin. Phys. B 18 1312

    [19]

    Ding G T 2009 Acta Phys. Sin. 58 7431(in Chinese) [丁光涛 2009 物理学报 58 7431]

    [20]

    Mei F X 1993 Science in China Serie A 36 1456

    [21]

    Mei F X, Zhang Y F, He G 2007 J Beijing Inst. Technol. 27 1035 (in Chinese) [梅凤翔、张永发、何 光 2007 北京理工大学学报 27 1035]

    [22]

    Mei F X, Xie J F, Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese) [梅凤翔、谢加芳、冮铁强 2008 物理学报 57 4649]

    [23]

    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]

    [24]

    Shang M, Mei F X 2009 Chin. Phys. B 18 3155

    [25]

    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]

    [26]

    Zhang Y 2009 Acta Phys. Sin. 58 7436(in Chinese)[张 毅 2009 物理学报 58 7436]

    [27]

    Mei F X, Liu D, Luo Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press)p333(in Chinese)[梅凤翔、刘 端、罗 勇 1991 高等分析力学(北京: 北京理工大学出版社)第333页]

    [28]

    Whittaker E T 1937 A Treatise on Analytical Dynamics of Particles and Rigid Bodies, Fouth Ed (Cambridge: Cambridge Univ Press)

    [29]

    Lurie A I 1961 Analyltical Mechanics (Moscow: GIFML) (in Russian)

    [30]

    José J V, Saletan E J 1998 Classical Dynanmics (New York: Cambridge vniv Press)

    [31]

    Papastavridis J G 2002 Analyltical Mechanics (New York: Oxford vniv Press)

    [32]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow:UFN) P183(in Russian)

  • [1]

    Santilli R M 1978 Foundations of theoretical mechanicsⅠ(New York: Springer Verlag)

    [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 Birkhoff Systems (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]

    Zhang H B 2001 Acta Phys. Sin. 50 1837(in Chinese)[张宏彬 2001 物理学报 50 1837]

    [5]

    Guo Y X, Luo S K, Shang M 2001 Rep. Math. Phys. 47 313

    [6]

    Luo S K, Lu Y B, Zhou Q, Wang Y D, Ou Y S 2002 Acta Phys. Sin. 51 1913(in Chinese)[罗绍凯、卢一兵、周 强、王应德、欧阳实2002 物理学报 51 1913]

    [7]

    Shang M, Guo Y X, Mei F X 2007 Chin. Phys. 16 292

    [8]

    Ge W K, Mei F X 2007 Acta Phys. Sin. 56 2476(in Chinese)[葛伟宽、梅凤翔2007 物理学报 56 2479]

    [9]

    Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678

    [10]

    Fu J L, Chen L Q, Luo S K, Chen X W, Wang X M 2001 Acta Phys. Sin. 50 2289(in Chinese)[傅景礼、陈立群、罗绍凯、陈向炜、王新民 2001 物理学报 50 2289]

    [11]

    Zhang Y 2008 Acta Phys. Sin. 57 5374(in Chinese)[张 毅2008 物理学报 57 5374]

    [12]

    Gu S L, Zhang H B 2004 Chin. Phys. 13 979

    [13]

    Ding N, Fang J H, Chen X X 2008 Chin. Phys. B 17 1967

    [14]

    Chen X W, Zhang R C, Mei F X 2000 Acta Mech. Sin. 16 282

    [15]

    Chen X W, Mei F X 2000 Mechanics Research Communications 27 365

    [16]

    Chen X W 2002 Chin. Phys. 11 441

    [17]

    Li Y M 2008 J. of Henan Normal University 36 52[李彦敏2008河南师范大学学报(自然科学版) 36 52]

    [18]

    Wang P, Fang J H, Wang X M 2009 Chin. Phys. B 18 1312

    [19]

    Ding G T 2009 Acta Phys. Sin. 58 7431(in Chinese) [丁光涛 2009 物理学报 58 7431]

    [20]

    Mei F X 1993 Science in China Serie A 36 1456

    [21]

    Mei F X, Zhang Y F, He G 2007 J Beijing Inst. Technol. 27 1035 (in Chinese) [梅凤翔、张永发、何 光 2007 北京理工大学学报 27 1035]

    [22]

    Mei F X, Xie J F, Gang T Q 2008 Acta Phys. Sin. 57 4649 (in Chinese) [梅凤翔、谢加芳、冮铁强 2008 物理学报 57 4649]

    [23]

    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]

    [24]

    Shang M, Mei F X 2009 Chin. Phys. B 18 3155

    [25]

    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]

    [26]

    Zhang Y 2009 Acta Phys. Sin. 58 7436(in Chinese)[张 毅 2009 物理学报 58 7436]

    [27]

    Mei F X, Liu D, Luo Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press)p333(in Chinese)[梅凤翔、刘 端、罗 勇 1991 高等分析力学(北京: 北京理工大学出版社)第333页]

    [28]

    Whittaker E T 1937 A Treatise on Analytical Dynamics of Particles and Rigid Bodies, Fouth Ed (Cambridge: Cambridge Univ Press)

    [29]

    Lurie A I 1961 Analyltical Mechanics (Moscow: GIFML) (in Russian)

    [30]

    José J V, Saletan E J 1998 Classical Dynanmics (New York: Cambridge vniv Press)

    [31]

    Papastavridis J G 2002 Analyltical Mechanics (New York: Oxford vniv Press)

    [32]

    Galiullin A S, Gafarov G G, Malaishka R P, Khwan A M 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow:UFN) P183(in Russian)

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  • 收稿日期:  2009-09-26
  • 修回日期:  2010-01-05
  • 刊出日期:  2010-04-05

一类广义Birkhoff系统的广义正则变换

  • 1. (1)北京理工大学宇航学院力学系,北京 100081; (2)商丘师范学院物理与信息工程系,商丘 476000
    基金项目: 

    国家自然科学基金(批准号: 10772025, 10932002, 10972127),河南省自然科学基金(批准号: 082300410330,082300410370,102300410144)资助的课题.

摘要: 研究一类广义Birkhoff系统的广义正则变换. 建立这类广义Birkhoff系统的运动微分方程, 得到了该系统的广义正则变换以及保持广义正则变换的条件. 最后, 举例说明结果的应用.

English Abstract

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