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讨论了构造Birkhoff表示的Hojman方法.利用该方法重新研究Birkhoff对称性,提出一种关于该对称性的新见解,给出Birkhoff守恒量的新证明,并对该守恒量仅与Birkhoff张量相关作出解释.举例说明所得结果的应用.
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关键词:
- Birkhoff系统 /
- 对称性 /
- 守恒量 /
- Hojman方法
[1] [1]Santilli R M 1983 Foundations of Theoretical Mechanics (Ⅱ) (New York: Springer-Verlag)
[2] [2]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)]
[3] [3]Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京:北京理工大学出版社)]
[4] [4]Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) pp288—415 (in Chinese) [罗绍凯、张永发 2008 约束系统动力学研究进展(北京:科学出版社) 第288—415页]
[5] [5]Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[6] [6]Mei F X 2009 Adv. Mech. 39 37 (in Chinese) [梅凤翔 2009 力学进展 39 37]
[7] [7]Mei F X 1993 Sci. China A 36 1456
[8] [8]Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 物理学报 51 461]
[9] [9]Gu S L, Zhang H B 2004 Chin. Phys. 13 979
[10] ]Zhang R C, Chen X W, Mei F X 2001 Chin. Phys. 10 12
[11] ]Xu X J, Mei F X, Qin M C 2004 Chin. Phys. 13 1999
[12] ]Zhang Y 2002 Chin. Phys. 11 437
[13] ]Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1986
[14] ]Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 物理学报 57 7415]
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[1] [1]Santilli R M 1983 Foundations of Theoretical Mechanics (Ⅱ) (New York: Springer-Verlag)
[2] [2]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)]
[3] [3]Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京:北京理工大学出版社)]
[4] [4]Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) pp288—415 (in Chinese) [罗绍凯、张永发 2008 约束系统动力学研究进展(北京:科学出版社) 第288—415页]
[5] [5]Mei F X, Gang T Q, Xie J F 2006 Chin. Phys. 15 1678
[6] [6]Mei F X 2009 Adv. Mech. 39 37 (in Chinese) [梅凤翔 2009 力学进展 39 37]
[7] [7]Mei F X 1993 Sci. China A 36 1456
[8] [8]Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 物理学报 51 461]
[9] [9]Gu S L, Zhang H B 2004 Chin. Phys. 13 979
[10] ]Zhang R C, Chen X W, Mei F X 2001 Chin. Phys. 10 12
[11] ]Xu X J, Mei F X, Qin M C 2004 Chin. Phys. 13 1999
[12] ]Zhang Y 2002 Chin. Phys. 11 437
[13] ]Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1986
[14] ]Ding G T 2008 Acta Phys. Sin. 57 7415 (in Chinese) [丁光涛 2008 物理学报 57 7415]
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