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The Hénon-Heiles equation that is nonlinear nonintegrable Hamilton system is studied by using the method of discrete variational valculation in the Birkhoffian sense. And the result from the method is compared with the result obtained by using symplectic algorithm and Runge-Kutta method, indicating that the method presented in this paper is reasonable and feasible in computing the dynamical action of the nonlinear nonintegrable Hamilton system in the Birkhoffian sense.
[1] Gleick J 1988 Chaos: Making a New Science (New York: Penguin Books)
[2] Hénen M,Heiles C 1964 J. Astronom. 69 73
[3] Maciejewski A J, Przybylska M 2004 Phys. Lett. A 327 461
[4] Morales-Ruiz J J, Simó C, Simon S 2005 Ergod. Ther. Dynam. Syst. 25 1237
[5] Morales-Ruiz J J, Ramis J P, Simon S 2007 Annales Scientiques de l’école Normale Supéieure 40 845
[6] Wen S H 2009 Acta Phys. Sin. 58 5209 (in Chinese) [温淑焕 2009 58 5209]
[7] Li S J, Peng S J 2009 Sci. Chin. A 52 2185
[8] Liu F C, Zhang Y L, Chen C 2008 Acta Phys. Sin. 57 2784 (in Chinese) [刘福才、张彦柳、陈 超 2008 57 2784]
[9] Birkhoff G D 1927 Dynamical Systems (Providence: American Mathematies Society College Publications)
[10] Li Y M,Mei F X 2010 Acta Phys. Sin. 59 5930 (in Chinese)[李彦敏、梅凤翔 2010 59 5930]
[11] Santilli R M 1978 Foundations of Theoretical MechanicsⅠ: The Inverse Problem in Newtonian Mechanics(New York: Springer)
[12] Santilli R M 1983 Foundations of Theoretical MechanicsⅡ: Birkhoffian Generalization of Hamiltonian Mechanics(New York: Springer)
[13] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoff Systems (Beijing: Beijing Institute of Technology Press)
[14] Liu S X, Liu C, Guo Y X 2010 Chin. Phys. B 19 030302
[15] Marsden J E, West M 2001 Acta Numerica (Vol. 10 ) (Cambridge: University of Cambridge) p357
[16] Hairer E, Lubich C, Wanner G 2002 Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Vol. 31 ) (Berlin: Springer)
[17] Cortes J 2002 Geometric, Control and Numerical Aspects of Nonholonomic Systems (Berlin: Springer)
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[1] Gleick J 1988 Chaos: Making a New Science (New York: Penguin Books)
[2] Hénen M,Heiles C 1964 J. Astronom. 69 73
[3] Maciejewski A J, Przybylska M 2004 Phys. Lett. A 327 461
[4] Morales-Ruiz J J, Simó C, Simon S 2005 Ergod. Ther. Dynam. Syst. 25 1237
[5] Morales-Ruiz J J, Ramis J P, Simon S 2007 Annales Scientiques de l’école Normale Supéieure 40 845
[6] Wen S H 2009 Acta Phys. Sin. 58 5209 (in Chinese) [温淑焕 2009 58 5209]
[7] Li S J, Peng S J 2009 Sci. Chin. A 52 2185
[8] Liu F C, Zhang Y L, Chen C 2008 Acta Phys. Sin. 57 2784 (in Chinese) [刘福才、张彦柳、陈 超 2008 57 2784]
[9] Birkhoff G D 1927 Dynamical Systems (Providence: American Mathematies Society College Publications)
[10] Li Y M,Mei F X 2010 Acta Phys. Sin. 59 5930 (in Chinese)[李彦敏、梅凤翔 2010 59 5930]
[11] Santilli R M 1978 Foundations of Theoretical MechanicsⅠ: The Inverse Problem in Newtonian Mechanics(New York: Springer)
[12] Santilli R M 1983 Foundations of Theoretical MechanicsⅡ: Birkhoffian Generalization of Hamiltonian Mechanics(New York: Springer)
[13] Mei F X, Shi R C, Zhang Y F, Wu H B 1996 Dynamics of Birkhoff Systems (Beijing: Beijing Institute of Technology Press)
[14] Liu S X, Liu C, Guo Y X 2010 Chin. Phys. B 19 030302
[15] Marsden J E, West M 2001 Acta Numerica (Vol. 10 ) (Cambridge: University of Cambridge) p357
[16] Hairer E, Lubich C, Wanner G 2002 Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Vol. 31 ) (Berlin: Springer)
[17] Cortes J 2002 Geometric, Control and Numerical Aspects of Nonholonomic Systems (Berlin: Springer)
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