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Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature

  • Book
  • © 2003

Overview

Authors:
  1. Tatiana G. Vozmischeva

    1. Department of Applied Mathematics, Izhevsk State Technical University, Izhevsk, Russia

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Part of the book series: Astrophysics and Space Science Library (ASSL, volume 295)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Basic Concepts and Theorems

    • Tatiana G. Vozmischeva
    Pages 1-36

  3. Generalization of the Kepler Problem to Spaces of Constant Curvature

    • Tatiana G. Vozmischeva
    Pages 37-80

  4. The Two-Center Problem on a Sphere

    • Tatiana G. Vozmischeva
    Pages 81-132

  5. The Two-Center Problem in the Lobachevsky Space

    • Tatiana G. Vozmischeva
    Pages 133-157

  6. Motion in Newtonian and Homogeneous Field in the Lobachevsky Space

    • Tatiana G. Vozmischeva
    Pages 159-172

  7. Back Matter

    Pages 173-184
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Applied Mathematics, Izhevsk State Technical University, Izhevsk, Russia

    Tatiana G. Vozmischeva

Bibliographic Information

  • Book Title: Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature

  • Authors: Tatiana G. Vozmischeva

  • Series Title: Astrophysics and Space Science Library

  • DOI: https://doi.org/10.1007/978-94-017-0303-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2003

  • Hardcover ISBN: 978-1-4020-1521-2Published: 31 October 2003

  • Softcover ISBN: 978-90-481-6382-3Published: 25 December 2010

  • eBook ISBN: 978-94-017-0303-1Published: 17 April 2013

  • Series ISSN: 0067-0057

  • Series E-ISSN: 2214-7985

  • Edition Number: 1

  • Number of Pages: XI, 184

  • Topics: Astronomy, Observations and Techniques, Geometry

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