Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

  • Kenneth R. Meyer
  • Glen R. Hall
Book

Part of the Applied Mathematical Sciences book series (AMS, volume 90)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Kenneth R. Meyer, Glen R. Hall
    Pages 1-32
  3. Kenneth R. Meyer, Glen R. Hall
    Pages 33-71
  4. Kenneth R. Meyer, Glen R. Hall
    Pages 72-86
  5. Kenneth R. Meyer, Glen R. Hall
    Pages 87-108
  6. Kenneth R. Meyer, Glen R. Hall
    Pages 109-153
  7. Kenneth R. Meyer, Glen R. Hall
    Pages 154-167
  8. Kenneth R. Meyer, Glen R. Hall
    Pages 168-200
  9. Kenneth R. Meyer, Glen R. Hall
    Pages 201-226
  10. Kenneth R. Meyer, Glen R. Hall
    Pages 227-240
  11. Kenneth R. Meyer, Glen R. Hall
    Pages 241-278
  12. Back Matter
    Pages 279-294

About this book

Introduction

This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincaré's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods.

The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point.

Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University.

Keywords

Dynamical Hamiltonian Mathematics N-Body Problem differential equation

Authors and affiliations

  • Kenneth R. Meyer
    • 1
  • Glen R. Hall
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Mathematics DepartmentBoston UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4073-8
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-4075-2
  • Online ISBN 978-1-4757-4073-8
  • Series Print ISSN 0066-5452
  • About this book
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