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The generalized Birkhoff equations are obtained by using supplementary terms added to the Birkhoff equations. An integral of the Birkhoff equations can be used to the generalized Birkhoff equations.An example is given to illustrate the application of the result.
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Keywords:
- Birkhoff equations /
- generalized Birkhoff equations /
- integral
[1] Santilli R M 1983 Foundations of Theoretical Mechanics II(NewYork:Springer-Verlag)
[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] Galiullin A S, Gafarov G G, Malaishka R P, Khwan AM 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow:RZUFN) (in Russian)
[4] Chen X W 2002 Global Analysis of Birkhoff System (Kaifeng:Henan Univ. Press) (in Chinese) [陈向炜2002 Birkhoff系统的全局分析 (开封:河南大学出版社)]
[5] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张 毅、梅凤翔 2004 物理学报53 2419]
[6] Xu Z X 2005 Acta Phys. Sin. 54 4971 (in Chinese) [许志新 2005 物理学报54 4971]
[7] Zhang H B,Gu S L 2002 Chin. Phys. 11 765
[8] Luo S K, Cai J L 2003 Chin. Phys. 12 357
[9] Xu X J, Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[10] Fu J L, Chen L Q, Xue F P 2003 Acta Phys. Sin. 52 2664 (in Chinese)[傅景礼、陈立群、谢凤萍 2003 物理学报 52 2664]
[11] Zhang P Y, Fang J H 2006 Acta Phys. Sin. 55 3813 (in Chinese)[张鹏玉、方建会 2006 物理学报55 3813]
[12] Mei F X,Gang T Q,Xie J F 2006 Chin. Phys. 15 1678
[13] Mei F X 1993 Sience in China Ser. A 36 1456
[14] Mei F X,Zhang Y F,He G,Gang T Q,Xie J F 2007 J. of 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]
[15] 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]
[16] 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]
[17] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583
[18] 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]
[19] Zhang Y 2009 Acta Phys. Sin. 58 7436 (in Chinese) [张 毅 2009 物理学报 58 7436]
[20] Shang M, Mei F X 2009 Chin. Phys. B 18 3155
[21] Li YM,Mei F X 2010 Acta Phys. Sin. 59 5219 (in Chinese) [李彦敏、梅凤翔 2010 物理学报59 5219]
[22] Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[23] Li YM, Mei F X 2010 Chin. Phys. B 19 080302
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[1] Santilli R M 1983 Foundations of Theoretical Mechanics II(NewYork:Springer-Verlag)
[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] Galiullin A S, Gafarov G G, Malaishka R P, Khwan AM 1997 Analytical Dynamics of Helmholtz, Birkhoff and Nambu Systems (Moscow:RZUFN) (in Russian)
[4] Chen X W 2002 Global Analysis of Birkhoff System (Kaifeng:Henan Univ. Press) (in Chinese) [陈向炜2002 Birkhoff系统的全局分析 (开封:河南大学出版社)]
[5] Zhang Y, Mei F X 2004 Acta Phys. Sin. 53 2419 (in Chinese) [张 毅、梅凤翔 2004 物理学报53 2419]
[6] Xu Z X 2005 Acta Phys. Sin. 54 4971 (in Chinese) [许志新 2005 物理学报54 4971]
[7] Zhang H B,Gu S L 2002 Chin. Phys. 11 765
[8] Luo S K, Cai J L 2003 Chin. Phys. 12 357
[9] Xu X J, Mei F X,Qin M C 2004 Chin. Phys. 13 1999
[10] Fu J L, Chen L Q, Xue F P 2003 Acta Phys. Sin. 52 2664 (in Chinese)[傅景礼、陈立群、谢凤萍 2003 物理学报 52 2664]
[11] Zhang P Y, Fang J H 2006 Acta Phys. Sin. 55 3813 (in Chinese)[张鹏玉、方建会 2006 物理学报55 3813]
[12] Mei F X,Gang T Q,Xie J F 2006 Chin. Phys. 15 1678
[13] Mei F X 1993 Sience in China Ser. A 36 1456
[14] Mei F X,Zhang Y F,He G,Gang T Q,Xie J F 2007 J. of 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]
[15] 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]
[16] 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]
[17] Mei F X, Xie J F, Gang T Q 2008 Acta Mech. Sin. 24 583
[18] 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]
[19] Zhang Y 2009 Acta Phys. Sin. 58 7436 (in Chinese) [张 毅 2009 物理学报 58 7436]
[20] Shang M, Mei F X 2009 Chin. Phys. B 18 3155
[21] Li YM,Mei F X 2010 Acta Phys. Sin. 59 5219 (in Chinese) [李彦敏、梅凤翔 2010 物理学报59 5219]
[22] Mei F X, Wu H B 2010 Chin. Phys. B 19 050301
[23] Li YM, Mei F X 2010 Chin. Phys. B 19 080302
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