Symplectification of truncated maps for Hamiltonian systems

被引：9

作者：

Andrianov, S ^{[1
]}

机构：

[1] St Petersburg State Univ, St Petersburg 198904, Russia

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2001年 / 57卷 / 3-5期

关键词：

Hamiltonian maps; Lie algebraic methods; symplectic maps; exact symplectic conditions; computer algebra;

D O I：

10.1016/S0378-4754(01)00333-0

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The time-displacement operator for Hamiltonian dynamical systems M(t \t(0)) is a symplectic transformation Lie map. Any truncated Lie map (Lie approximant) loses the very important symplectic property. In this report a method of correcting the truncated map is given. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of simple linear algebraic equations. The symbolic solutions of these equations are computed in advance and are stored in a database. This approach allows us to simplify the calculation process for the evolution of dynamical systems, in particular, for long time evolution. (C) 2001 Published by Elsevier Science B.V. on behalf of IMACS.

引用

页码：139 / 145

页数：7