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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.
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关键词:
- 广义Birkhoff系统 /
- 广义正则变换 /
- 生成函数
The generalized canonical transformations of a kind of generalized Birkhoff systems are studied in this paper. The differential equations of motion of the generalized Birkhoff systems are estallished. The condition under which the transformations of the system are canonical is obtained. An example is given to illustrate the application of the result.[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 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 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 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 50 2289]
[11] Zhang Y 2008 Acta Phys. Sin. 57 5374(in Chinese)[张 毅2008 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 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 57 4649]
[23] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657(in Chinese) [梅凤翔、蔡建乐2008 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 58 699]
[26] Zhang Y 2009 Acta Phys. Sin. 58 7436(in Chinese)[张 毅 2009 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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[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 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 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 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 50 2289]
[11] Zhang Y 2008 Acta Phys. Sin. 57 5374(in Chinese)[张 毅2008 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 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 57 4649]
[23] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4657(in Chinese) [梅凤翔、蔡建乐2008 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 58 699]
[26] Zhang Y 2009 Acta Phys. Sin. 58 7436(in Chinese)[张 毅 2009 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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