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The method of constructing Birkhoffian funcations of mechanical systems is investigated. The redundant term is discovered in Santilli's second method. As a result, a simpler construction formula for self-adjoint systems is obtained by cancelling the redundant term. An example is given to illustrate the application of the results.
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Keywords:
- Birkhoffian systems /
- Birkhoffian funcations /
- Santilli
[1] Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York: Springer-Verlag)
[2] Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1896
[3] [4] [5] 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)]
[6] Guo Y X, Liu C, Liu S X 2011 Commun. Math. 18 21
[7] [8] Ding G T 2010 Acta. Phys. Sin. 59 3643 (in Chinese) [丁光涛 2010 59 3643]
[9] [10] [11] Wu H B, Mei F X 2011 Chin. Phys. B 10 290
[12] [13] Zhang Y, Xue Y 2009 Chin. Quar. Mech. 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[14] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[15] [16] [17] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[18] [19] Chen X W 2002 Global Analysis of Birkhoffian System (Kaifeng: Henan University Press) (in Chinese) [陈向炜 2002 Birkhoff系统的全局分析 (开封: 河南大学出版社)]
[20] Liu S X, Liu C, Guo Y X 2011 Chin. Phys. B 20 034501
[21] [22] Liu C, Liu S X, Guo Y X 2011 Sci. Chin. Tech. Sci. 54 2100
[23] [24] [25] Cui J C, Liu S X, Song D 2013 Chin. Phys. B 22 104501
[26] [27] Kong X L, Wu H B, Mei F X 2013 Nonlinear Dyn. 74 711
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[1] Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York: Springer-Verlag)
[2] Hojman S, Urrutia L F 1981 J. Math. Phys. 22 1896
[3] [4] [5] 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)]
[6] Guo Y X, Liu C, Liu S X 2011 Commun. Math. 18 21
[7] [8] Ding G T 2010 Acta. Phys. Sin. 59 3643 (in Chinese) [丁光涛 2010 59 3643]
[9] [10] [11] Wu H B, Mei F X 2011 Chin. Phys. B 10 290
[12] [13] Zhang Y, Xue Y 2009 Chin. Quar. Mech. 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[14] Luo S K, Li Z J, Li L 2012 Acta Mechanica 223 2621
[15] [16] [17] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[18] [19] Chen X W 2002 Global Analysis of Birkhoffian System (Kaifeng: Henan University Press) (in Chinese) [陈向炜 2002 Birkhoff系统的全局分析 (开封: 河南大学出版社)]
[20] Liu S X, Liu C, Guo Y X 2011 Chin. Phys. B 20 034501
[21] [22] Liu C, Liu S X, Guo Y X 2011 Sci. Chin. Tech. Sci. 54 2100
[23] [24] [25] Cui J C, Liu S X, Song D 2013 Chin. Phys. B 22 104501
[26] [27] Kong X L, Wu H B, Mei F X 2013 Nonlinear Dyn. 74 711
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