Symmetries and variational calculationof discrete Hamiltonian systems

doi:10.1088/1674-1056/23/7/070201

›› 2014, Vol. 23 ›› Issue (7): 70201-070201.doi: 10.1088/1674-1056/23/7/070201

• GENERAL • 下一篇

Symmetries and variational calculationof discrete Hamiltonian systems

夏丽莉^{a b}, 陈立群^{b c d}, 傅景礼^e, 吴旌贺^a

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

收稿日期:2013-10-17 修回日期:2014-01-26 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
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).

Symmetries and variational calculationof discrete Hamiltonian systems

Xia Li-Li (夏丽莉)^{a b}, Chen Li-Qun (陈立群)^{b c d}, Fu Jing-Li (傅景礼)^e, Wu Jing-He (吴旌贺)^a

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

Received:2013-10-17 Revised:2014-01-26 Online:2014-07-15 Published:2014-07-15
Contact: Chen Li-Qun E-mail:lqchen@straff.shu.edu.cn
About author:02.20.Sv; 02.20.Qs; 11.30.-j; 45.20.Jj
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: discrete Hamiltonian systems, discrete variational integrators, symmetry, conserved quantity

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.

Key words: discrete Hamiltonian systems, discrete variational integrators, symmetry, conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

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)

夏丽莉, 陈立群, 傅景礼, 吴旌贺. Symmetries and variational calculationof discrete Hamiltonian systems[J]. , 2014, 23(7): 70201-070201.

Xia Li-Li (夏丽莉), Chen Li-Qun (陈立群), Fu Jing-Li (傅景礼), Wu Jing-He (吴旌贺). Symmetries and variational calculationof discrete Hamiltonian systems[J]. Chin. Phys. B, 2014, 23(7): 70201-070201.

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Symmetries and variational calculationof discrete Hamiltonian systems

Symmetries and variational calculationof discrete Hamiltonian systems

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