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Chin. Phys. B, 2014, Vol. 23(7): 070201    DOI: 10.1088/1674-1056/23/7/070201
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Symmetries and variational calculationof discrete Hamiltonian systems

Xia Li-Lia b, Chen Li-Qunb c d, Fu Jing-Lie, Wu Jing-Hea
a Department of Physics, Henan Institute of Education, Zhengzhou 450046, China;
b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
c Department of Mechanics, Shanghai University, Shanghai 200444, China;
d Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China;
e Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.
Keywords:  discrete Hamiltonian systems      discrete variational integrators      symmetry      conserved quantity     
Received:  17 October 2013      Published:  15 July 2014
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.20.Qs (General properties, structure, and representation of Lie groups)  
  11.30.-j (Symmetry and conservation laws)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
Fund: Project supported by the Key Program of National Natural Science Foundation of China (Grant No. 11232009), the National Natural Science Foundation of China (Grant Nos. 11072218, 11272287, and 11102060), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), the Natural Science Foundation of Henan Province, China (Grant No. 132300410051), and the Educational Commission of Henan Province, China (Grant No. 13A140224).
Corresponding Authors:  Chen Li-Qun     E-mail:  lqchen@straff.shu.edu.cn
About author:  02.20.Sv; 02.20.Qs; 11.30.-j; 45.20.Jj

Cite this article: 

Xia Li-Li, Chen Li-Qun, Fu Jing-Li, Wu Jing-He Symmetries and variational calculationof discrete Hamiltonian systems 2014 Chin. Phys. B 23 070201

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