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基于哈密顿动力系统新变分原理的保辛算法之二:算法保辛性质证明
引用本文:高强,彭海军,张洪武,钟万勰.基于哈密顿动力系统新变分原理的保辛算法之二:算法保辛性质证明[J].计算力学学报,2013,30(4):468-472.
作者姓名:高强  彭海军  张洪武  钟万勰
作者单位:大连理工大学工业装备结构分析国家重点实验室,工程力学系,大连116024
基金项目:国家自然科学基金(11272076,10721062);973项目(2011CB711105,2010CB832704);中央高校基本科研业务费专项基金(DUT13LK12)资助项目.
摘    要:文献1]给出了哈密顿系统的一个新的变分原理,并基于此变分原理,通过选择一个时间步长两端不同广义位移或广义动量为独立变量,给出了四种不同类型的求解哈密顿动力系统的数值方法。本文将分别证明这四类数值方法都是保辛的数值方法。

关 键 词:保辛  哈密顿系统  变分原理  作用量
收稿时间:2012/2/10 0:00:00
修稿时间:2012/7/15 0:00:00

The symplectic algorithms for Hamiltonian dynamic systems based on a new variational principle part II:the proof of the symplecticity
GAO Qiang,PENG Hai-jun,ZHANG Hong-wu and ZHONG Wan-xie.The symplectic algorithms for Hamiltonian dynamic systems based on a new variational principle part II:the proof of the symplecticity[J].Chinese Journal of Computational Mechanics,2013,30(4):468-472.
Authors:GAO Qiang  PENG Hai-jun  ZHANG Hong-wu and ZHONG Wan-xie
Institution:State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China;State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China
Abstract:In Reference 1],a new variational principle for the finite dimensional autonomous Hamiltonian systems was proposed.Based on this new variational principle and by taking generalized coordinates or momenta as independent variables at each end of the time step,four types of numerical algorithms were constructed.In this paper,the proof of symplectic property of the four of numerical algorithms is given.
Keywords:symplectic  Hamiltonian system  variational principle  action
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