| 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,2013,30(4):461~467 |
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| 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 |
| 投稿时间：2012-02-10 修订日期：2012-07-15 |
| DOI：10.7511/jslx201304001 |
| 中文关键词: 保辛 哈密顿系统 变分原理 作用量 |
| 英文关键词:symplectic Hamiltonian system variational principle action |
| 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. |
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| 中文摘要: |
| 提出了哈密顿动力系统的一个新变分原理,并基于此变分原理构造了四类保辛算法。通过新的变分原理定义修正作用量,然后将位移和动量采用拉格朗日多项式近似,并采用高斯积分对时间近似积分得到近似的修正作用量。在修正作用量的基础上,通过选择时间步两端不同的位移或动量作为独立变量,可构造四种不同类型的保辛算法。 |
| 英文摘要: |
| 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 action is defined by using the new variational principle.Then,the approximated action is obtained by approximating 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 performance of the algorithms will present in other papers. |
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