A First Order Automated Lie Transform

被引：41

作者：

Abouelmagd, Elbaz I. ^{[1
]}

Mostafa, A. ^{[2
]}

Guirao, Juan L. G. ^{[3
]}

机构：

[1] Natl Res Inst Astron & Geophys, Cairo, Egypt

[2] Ain Shams Univ, Fac Sci, Dept Math, Cairo, Egypt

[3] Tech Univ Cartagena, Hosp Marina, Dept Appl Math & Stat, Cartagena 30203, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 14期

关键词：

Lie transform; Hamiltonian system; dynamical systems; GENERAL PLANETARY THEORY; ARTIFICIAL-SATELLITES; BODY PROBLEM; MOTION; SERIES; EQUATIONS; PERTURBATIONS; CONSTRUCTION; INTEGRATION; STABILITY;

D O I：

10.1142/S021812741540026X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The objective of the present paper is to focus on the problem of the normalization of a Hamiltonian system via the elimination of angle variables involved using the Lie transform technique. The algorithm that we construct assumes that the Hamiltonian is periodic in n angle variables, with two rates: fast and slow. If the angle variables have the same rate only one transformation is required. The equations needed to evaluate the elements of each transformation and the secular perturbations are constructed.

引用

页数：10

共 32 条

[1] Numerical integration of the restricted three-body problem with Lie series [J].