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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

  • Kenneth R. Meyer
  • Daniel C. Offin

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Kenneth R. Meyer, Daniel C. Offin
    Pages 1-27
  3. Kenneth R. Meyer, Daniel C. Offin
    Pages 29-60
  4. Kenneth R. Meyer, Daniel C. Offin
    Pages 61-81
  5. Kenneth R. Meyer, Daniel C. Offin
    Pages 83-102
  6. Kenneth R. Meyer, Daniel C. Offin
    Pages 103-141
  7. Kenneth R. Meyer, Daniel C. Offin
    Pages 143-168
  8. Kenneth R. Meyer, Daniel C. Offin
    Pages 169-193
  9. Kenneth R. Meyer, Daniel C. Offin
    Pages 195-224
  10. Kenneth R. Meyer, Daniel C. Offin
    Pages 225-238
  11. Kenneth R. Meyer, Daniel C. Offin
    Pages 239-278
  12. Kenneth R. Meyer, Daniel C. Offin
    Pages 279-303
  13. Kenneth R. Meyer, Daniel C. Offin
    Pages 305-344
  14. Kenneth R. Meyer, Daniel C. Offin
    Pages 345-372
  15. Back Matter
    Pages 373-384

About this book

Introduction

This third edition text provides expanded material on the restricted three body problem and celestial mechanics.  With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications.

The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different 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.

This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike.


Reviews of the second edition:

"The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. … It is a well-organized and accessible introduction to the subject … . This is an attractive book … ." (William J. Satzer, The Mathematical Association of America, March, 2009)

“The second edition of this text infuses new mathematical substance and relevance into an already modern classic … and is sure to excite future generations of readers. … This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. … it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)

Keywords

Hamiltonian Systems Dynamical Systems Symplectic Hamiltonian Matrices Restricted 3-body Problem Periodic Solutions KAM Theory Variational Methods

Authors and affiliations

  • Kenneth R. Meyer
    • 1
  • Daniel C. Offin
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of Mathematic and StatisticsQueen’s UniversityKingstonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-53691-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-53690-3
  • Online ISBN 978-3-319-53691-0
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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