Lie symmetries and conserved quantities based on the variational integrators for the nonconservative Hamiltonian systems

doi:10.3969/j.issn.1000-1565.2019.01.002

Journal of Hebei University (Natural Science Edition) ›› 2019, Vol. 39 ›› Issue (1): 6-10.DOI: 10.3969/j.issn.1000-1565.2019.01.002

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Lie symmetries and conserved quantities based on the variational integrators for the nonconservative Hamiltonian systems

XIA Lili^1,2, GUO Zhongjin^1,3, ZHANG Wei²

1.School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China; 2.College of Mechaniacl Engineering, Beijing University of Technology, Beijing 100124, China; 3.School of Mathematics and Statistics, Taishan University, Taian 271000, China

Received:2018-10-17 Online:2019-01-25 Published:2019-01-25

Abstract

Abstract: The difference equations and the energy equation of the nonconservative Hamiltonian systems are proposed by introducing the discrete difference variational principle.The structure-preserving algorithms are proposed for these equations.The discrete determining equations of the Lie symmetries are obtained. The conserved quantities of the systems are given through the discrete Noether theorem. An example is given to illustrate the results.

Key words: nonconservative Hamiltonian systems, discrete difference variational principle, Lie symmetries, the conserved quantities

CLC Number:

O316

XIA Lili, GUO Zhongjin, ZHANG Wei. Lie symmetries and conserved quantities based on the variational integrators for the nonconservative Hamiltonian systems[J]. Journal of Hebei University (Natural Science Edition), 2019, 39(1): 6-10.

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Lie symmetries and conserved quantities based on the variational integrators for the nonconservative Hamiltonian systems

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