Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature

T. G. Vozmischeva

ISBN 10: 1402015216 / ISBN 13: 9781402015212

Published by Springer, Springer Okt 2003, 2003

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 200 pp. Englisch.

Seller Inventory # 9781402015212

Bibliographic Details

• Title: Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature
• Publisher: Springer, Springer Okt 2003
• Publication Date: 2003
• Language: English
• ISBN 10: 1402015216
• ISBN 13: 9781402015212
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 17D millimeters 241 millimeters width by 160 millimeters height by 17 millimeters depth
• Weight: 471 grams

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.