Global Aspects of Classical Integrable Systems

  • Richard H. Cushman
  • Larry M. Bates

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Examples

    1. Front Matter
      Pages 1-1
    2. Richard H. Cushman, Larry M. Bates
      Pages 3-32
    3. Richard H. Cushman, Larry M. Bates
      Pages 33-80
    4. Richard H. Cushman, Larry M. Bates
      Pages 81-140
    5. Richard H. Cushman, Larry M. Bates
      Pages 141-193
    6. Richard H. Cushman, Larry M. Bates
      Pages 195-282
  3. Theory

    1. Front Matter
      Pages 283-283
    2. Richard H. Cushman, Larry M. Bates
      Pages 285-308
    3. Richard H. Cushman, Larry M. Bates
      Pages 309-376
    4. Richard H. Cushman, Larry M. Bates
      Pages 377-387
    5. Richard H. Cushman, Larry M. Bates
      Pages 389-394
    6. Richard H. Cushman, Larry M. Bates
      Pages 395-425
    7. Richard H. Cushman, Larry M. Bates
      Pages 427-434
  4. Back Matter
    Pages 435-481

About this book

Introduction

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Keywords

algebra classical mechanics hamiltonian mechanics manifold pendulum

Authors and affiliations

  • Richard H. Cushman
    • 1
  • Larry M. Bates
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0918-4
  • Copyright Information Springer Basel 2015
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-0348-0917-7
  • Online ISBN 978-3-0348-0918-4
  • About this book