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Periodic Solutions of the N-Body Problem

  • Book
  • © 1999

Overview

Authors:
  1. Kenneth R. Meyer
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1719)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Kenneth R. Meyer
    Pages 1-8

  3. Equations of celestial mechanics

    • Kenneth R. Meyer
    Pages 9-18

  4. Hamiltonian systems

    • Kenneth R. Meyer
    Pages 19-37

  5. Central configurations

    • Kenneth R. Meyer
    Pages 39-49

  6. Symmetries, integrals, and reduction

    • Kenneth R. Meyer
    Pages 51-70

  7. Theory of periodic solutions

    • Kenneth R. Meyer
    Pages 71-86

  8. Satellite orbits

    • Kenneth R. Meyer
    Pages 87-90

  9. The restricted problem

    • Kenneth R. Meyer
    Pages 91-103

  10. Lunar orbits

    • Kenneth R. Meyer
    Pages 105-110

  11. Comet orbits

    • Kenneth R. Meyer
    Pages 111-118

  12. Hill’s lunar equations

    • Kenneth R. Meyer
    Pages 119-127

  13. The elliptic problem

    • Kenneth R. Meyer
    Pages 129-137

  14. Back Matter

    Pages 139-144
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Keywords

About this book

The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space.

Bibliographic Information

  • Book Title: Periodic Solutions of the N-Body Problem

  • Authors: Kenneth R. Meyer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094677

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-66630-1Published: 17 November 1999

  • eBook ISBN: 978-3-540-48073-0Published: 17 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 154

  • Topics: Global Analysis and Analysis on Manifolds

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