基于离散Legenda变换的Hamilton系统的变分算法和辛结构  

Variational calculation and symplectic structure of Hamiltonian systems based the discrete Legenda transformations

作　　者：夏丽莉[1,2] 国忠金[1,3] 张伟[1] XIA Lili GUO Zhongjin ZHANG Wei(College of Mechaniaei Engineering, Beijing University of Technology, Beijing 100124 College of Physical and Eeleetronie Engineering, Henan Institute of Education, Zhengzhou 45004 School of Mathematics and Statistics, Taishan University, Taian, Shandong 271000)

机构地区：[1]北京工业大学机械工程与应用电子技术学院,北京100124 [2]河南教育学院物理与电子工程学院,郑州450046 [3]泰山学院数学与统计学院,山东泰安271000

出　　处：《华中师范大学学报（自然科学版）》2017年第4期449-454,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11502071,11290152);北京市朝阳区博士后基金项目;河南省教育厅基础研究项目(17A140015)

摘　　要：根据动量的不同表达式,给出3种不同的Legenda变换形式;得到3种不同形式的Hamilton系统的动力学方程;给出辛结构守恒的具体形式;二自由度非线性谐振子的例子验证基于离散变分原理的算法具有保系统的能量守恒量性质.Three types of discrete Legenda transformations are obtained when the displacement coordinates are defined implicitly by different momentum.The different forms of Hamiltonian equations are constructed based on the difference Legenda transformations.The symplectic structures of the three Hamilton systems are given,respectively.The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show the advantage of variational numerical method.

关 键 词：差分离散变分原理 离散Legenda变换 变分算子 

分 类 号：O316[理学—一般力学与力学基础]