Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature

T. G. Vozmischeva

ISBN 10: 904816382X / ISBN 13: 9789048163823

Published by Springer, 2010

About this Item

Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature | T. G. Vozmischeva | Taschenbuch | Astrophysics and Space Science Library | xi | Englisch | 2010 | Springer | EAN 9789048163823 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

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Bibliographic Details

• Title: Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 904816382X
• ISBN 13: 9789048163823
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 12D millimeters 235 millimeters width by 155 millimeters height by 12 millimeters depth
• Weight: 312 grams
• Seller catalogs:
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About this title

Synopsis

Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al­ gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa­ tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce­ lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.