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

作　　者：夏丽莉 国忠金[2,3] 张伟 XIA Lili;GUO Zhongjin;ZHANG Wei(School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China;College of Mechaniacl Engineering, Beijing University of Technology, Beijing 100124,China;School of Mathematics and Statistics, Taishan University, Taian 271000, China)

机构地区：[1]北京信息科技大学理学院,北京100196 [2]北京工业大学机械工程与应用电子技术学院,北京100124 [3]泰山学院数学与统计学院,山东泰安271000

出　　处：《河北大学学报（自然科学版）》2019年第1期6-10,共5页Journal of Hebei University(Natural Science Edition)

基　　金：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)

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.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.

关 键 词：非保守Hamilton系统 差分离散变分原理 LIE对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]