Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

  • Kenneth Meyer
  • Glen Hall
  • Dan Offin

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

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 1-25
  3. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 27-44
  4. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 45-68
  5. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 69-115
  6. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 117-132
  7. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 133-145
  8. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 147-173
  9. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 175-216
  10. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 217-230
  11. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 231-270
  12. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 271-299
  13. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 301-327
  14. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 329-354
  15. Kenneth Meyer, Glen Hall, Dan Offin
    Pages 355-387
  16. Back Matter
    Pages 389-399

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 Meyer
    • 1
  • Glen Hall
    • 2
  • Dan Offin
    • 3
  1. 1.Department of MathematicsUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  3. 3.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-09724-4
  • Copyright Information Springer New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-09723-7
  • Online ISBN 978-0-387-09724-4
  • Series Print ISSN 0066-5452
  • About this book
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