基于离散变分算子的非保守Hamilton系统的Lie对称性与守恒量

doi:10.3969/j.issn.1000-1565.2019.01.002

河北大学学报(自然科学版) ›› 2019, Vol. 39 ›› Issue (1): 6-10.DOI: 10.3969/j.issn.1000-1565.2019.01.002

基于离散变分算子的非保守Hamilton系统的Lie对称性与守恒量

夏丽莉^1,2,国忠金^2,3,张伟²

收稿日期:2018-10-17 出版日期:2019-01-25 发布日期:2019-01-25
通讯作者: 张伟(1960—),男,天津人,北京工业大学教授,博士,主要从事动力学与控制方面的研究.E-mail: sandyzhang@yahoo.com
作者简介:夏丽莉(1980—),女,江苏徐州人,北京信息科技大学副教授,主要从事动力学系统的离散化和积分理论研究. E-mail: xll2004@126.com
基金资助:
国家自然科学基金资助项目(11502071;11290152);北京信息科技大学促进高校内涵发展科研水平提高项目;北京信息科技大学学校科研基金资助项目(1825024)

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

摘要/Abstract

摘要： 从力学的变分原理出发,得到了受非保守约束力的Hamilton系统的动力学方程的离散形式和能量演化方程,即保结构数值算法格式. 给出了非保守Hamilton系统的离散Lie对称性判定方程;基于离散Noether定理推导出系统Noether守恒量的离散形式. 最后举例说明本文结论的合理性.

关键词: 非保守Hamilton系统, 差分离散变分原理, Lie对称性, 守恒量

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

中图分类号:

O316

夏丽莉,国忠金,张伟. 基于离散变分算子的非保守Hamilton系统的Lie对称性与守恒量[J]. 河北大学学报(自然科学版), 2019, 39(1): 6-10.

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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基于离散变分算子的非保守Hamilton系统的Lie对称性与守恒量

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

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