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Global Aspects of Classical Integrable Systems

  • Book
  • © 2015

Overview

Authors:
  1. Richard H. Cushman

    1. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. Larry M. Bates

    1. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

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    You can also search for this author in PubMed   Google Scholar

  • This book gives a complete global geometric description of the motion of the two dimensional harmonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top

  • This book is necessary because the standard treatments are not complete

  • Main goal of this book is to understand the global geometric features of our model integrable systems

  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Examples

    1. Front Matter

      Pages 1-1
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    2. The harmonic oscillator

      • Richard H. Cushman, Larry M. Bates
      Pages 3-32

    3. Geodesics on S 3

      • Richard H. Cushman, Larry M. Bates
      Pages 33-80

    4. The Euler Top

      • Richard H. Cushman, Larry M. Bates
      Pages 81-140

    5. The spherical pendulum

      • Richard H. Cushman, Larry M. Bates
      Pages 141-193

    6. The Lagrange top

      • Richard H. Cushman, Larry M. Bates
      Pages 195-282

  3. Theory

    1. Front Matter

      Pages 283-283
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    2. Fundamental concepts

      • Richard H. Cushman, Larry M. Bates
      Pages 285-308

    3. Systems with Symmetry

      • Richard H. Cushman, Larry M. Bates
      Pages 309-376

    4. Ehresmann connections

      • Richard H. Cushman, Larry M. Bates
      Pages 377-387

    5. Action-angle coordinates

      • Richard H. Cushman, Larry M. Bates
      Pages 389-394

    6. Monodromy

      • Richard H. Cushman, Larry M. Bates
      Pages 395-425

    7. Basic Morse Theory

      • Richard H. Cushman, Larry M. Bates
      Pages 427-434

  4. Back Matter

    Pages 435-481
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Richard H. Cushman, Larry M. Bates

Bibliographic Information

  • Book Title: Global Aspects of Classical Integrable Systems

  • Authors: Richard H. Cushman, Larry M. Bates

  • DOI: https://doi.org/10.1007/978-3-0348-0918-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer Basel 2015

  • Hardcover ISBN: 978-3-0348-0917-7Published: 11 June 2015

  • eBook ISBN: 978-3-0348-0918-4Published: 01 June 2015

  • Edition Number: 2

  • Number of Pages: XVIII, 477

  • Number of Illustrations: 17 b/w illustrations, 69 illustrations in colour

  • Topics: Theoretical, Mathematical and Computational Physics

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