Global Aspects of Classical Integrable Systems / Edition 1

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Overview

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.

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Editorial Reviews

From the Publisher
"Ideal for someone who needs a thorough global understanding of one of these systems [and] who would like to learn some of the tools and language of modern geometric mechanics. The exercises at the end of each chapter are excellent. The book could serve as a good supplementary text for a graduate course in geometric mechanics."

—SIAM Review

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Product Details

  • ISBN-13: 9783764354855
  • Publisher: Birkhauser Basel
  • Publication date: 2/4/2004
  • Edition description: 1997
  • Edition number: 1
  • Pages: 435
  • Sales rank: 1,386,845
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.00 (d)

Table of Contents

Foreword
Introduction
I The harmonic oscillator
II Geodesics on S[superscript 3]
III The Euler top
IV The spherical pendulum
V The Lagrange top
App. A Fundamental concepts
App. B Systems with symmetry
App. C Ehresmann connections
App. D Action angle coordinates
App. E Basic Morse theory
Notes
References
Acknowledgements
Index
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