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By use of the method to construct the Lagrangian from the first integral, two families of Lagrangians and some Lagrangians and Hamiltonians are obtained for a class of Painleve equations.
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Keywords:
- Painleve equation /
- inverse problem /
- family of Lagrangians /
- first integral
[1] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Spinger-Verlag)
[2] Lopuszanski J 1999 the Inverse Variational Problem in Classical Mechanics (Singapore: World Scientific)
[3] Sarlet W 1982 J. Phys. A: Math. Gen. 15 1503
[4] Li Y Z, He Y Z 2000 Advances in Mathmatics 29 481 (in Chinese) [李叶舟, 何育赞 2000 数学进展 29 481]
[5] Choudhury A G, Guha P, Khanra B 2009 J. Math. Anal. Appl. 360 651
[6] Yasar E, Reis M 2010 J. Phys. A: Math. Theor. 43 295202
[7] Ding G T 2011 Journal of Dynamics and Control 9 102 (in Chinese) [丁光涛 2011 动力学与控制学报 9 102]
[8] Ding G T 2011 Journal of Dynamics and Control 9 219 (in Chinese) [丁光涛 2011 动力学与控制学报 9 219]
[9] Musielak Z E 2008 J. Phys. A: Math. Theor. 41 055205
[10] Cieśliński J L, Nikiciuk T 2010 J. Phys. A: Math. Theor. 43 175205
[11] Ding G T 1996 J. Anhui Normal Univ. 19 382 (in Chinese) [丁光涛 1996 安徽师范大学学报 19 382]
[12] Ding G T 2011 Acta Phys. Sin. 60 044503 (in Chinese) [丁光涛 2011 60 044503]
[13] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (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)]
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[1] Santilli R M 1978 Foundations of Theoretical Mechanics I (New York: Spinger-Verlag)
[2] Lopuszanski J 1999 the Inverse Variational Problem in Classical Mechanics (Singapore: World Scientific)
[3] Sarlet W 1982 J. Phys. A: Math. Gen. 15 1503
[4] Li Y Z, He Y Z 2000 Advances in Mathmatics 29 481 (in Chinese) [李叶舟, 何育赞 2000 数学进展 29 481]
[5] Choudhury A G, Guha P, Khanra B 2009 J. Math. Anal. Appl. 360 651
[6] Yasar E, Reis M 2010 J. Phys. A: Math. Theor. 43 295202
[7] Ding G T 2011 Journal of Dynamics and Control 9 102 (in Chinese) [丁光涛 2011 动力学与控制学报 9 102]
[8] Ding G T 2011 Journal of Dynamics and Control 9 219 (in Chinese) [丁光涛 2011 动力学与控制学报 9 219]
[9] Musielak Z E 2008 J. Phys. A: Math. Theor. 41 055205
[10] Cieśliński J L, Nikiciuk T 2010 J. Phys. A: Math. Theor. 43 175205
[11] Ding G T 1996 J. Anhui Normal Univ. 19 382 (in Chinese) [丁光涛 1996 安徽师范大学学报 19 382]
[12] Ding G T 2011 Acta Phys. Sin. 60 044503 (in Chinese) [丁光涛 2011 60 044503]
[13] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (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)]
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