Integrable systems in celestial mechanics.
type: Item
instance of: scholarly article
title: Integrable systems in celestial mechanics.
zbMATH Open document ID: 1156.70002
author: Diarmuid Ó Mathúna
published in: Progress in Mathematical Physics
publication date: 2008-06-30T00:00:00Z
review text: The author considers three famous problems of celestial mechanics and space dynamics, i.e. the Kepler problem, the Euler problem and the (near Earth) artificial satellite problem which admit a complete analytic integration of the equations of motion. The book aims to show that the solutions of the mentioned problems admit a general representation and, more important, that the three problems share a common pattern. The monograph consists of a preface, general introduction and six chapters: 0. General introduction. Ch. 1. Lagrangian mechanics. 2. The Kepler problem. The Kepler problem is analyzed with the same reduction procedure applied to the rest problems. Ch. 3. The Euler problem I -- Planar case. This central chapter of the book gives a full analysis of the planar Euler problem, yielding an exact solution in terms of Jacobi elliptic functions. Ch. 4. The Euler problem II -- The three-dimensional case. It is shown that for two of the coordinates, the solution by algebraic transformations can be reduced to the planar case. The formula for the third coordinate (longitude) involving an elliptic integral of the third kind is shown to be amenable to an approximation procedure. Ch. 5. The Earth satellite -- general analysis. In Chapter 5, the author carries out the corresponding analysis and gives a reduction of Vinti problem. Ch. 6. The Earth satellite -- Some special orbits. This chapter deals with certain orbits of Vinti problem that require a special attention. Appendix: Calculation and exibition of orbits; The time-angle relation. There are 66 references.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70-02
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70F05
Mathematics Subject Classification ID: 70H06
Mathematics Subject Classification ID: 70M20
zbMATH DE Number: 5294598
zbMATH Keywords: dimension reduction
zbMATH Keywords: Kepler problem
zbMATH Keywords: Euler problem
zbMATH Keywords: Vinti problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5294598