计算力学学报Issue(4)：461-467,7.DOI:10.7511/jslx201304001
基于哈密顿动力系统新变分原理的保辛算法之一：变分原理和算法构造
The symplectic algorithms for Hamiltonian dynamic systems based on a new variational principle part I：the variational principle and the algorithms
摘要
Abstract
In this paper ,a new variational principle is proposed for the finite dimensional autonomous Hamiltonian systems and four types of symplecitc numerical algorithms are constructed .A modified ac-tion is defined by using the new variational principle .T hen ,the approximated action is obtained by ap-proximating the generalized coordinates and momenta by Lagrange polynomials within a time step ,and approximating the time integrals by means of Gaussian quadrature .Based on the approximated action and by taking generalized coordinates or momenta as independent variables at each end of the time step ,four types of symplecitc numerical algorithms are constructed .In this paper ,the detailed procedure for the construction of the algorithms is given and the proof of symplectic property and the numerical perform-ance of the algorithms will present in other papers .关键词
保辛/哈密顿系统/变分原理/作用量Key words
symplectic/Hamiltonian system/variational principle/action分类
数理科学引用本文复制引用
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一：变分原理和算法构造[J].计算力学学报,2013,(4):461-467,7.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． （）
