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Introduction to Mechanics and Symmetry

Introduction to Mechanics and Symmetry - 2nd edition

ISBN13: 978-0387986432

Cover of Introduction to Mechanics and Symmetry 2ND 99 (ISBN 978-0387986432)
ISBN13: 978-0387986432
ISBN10: 038798643X
Cover type:
Edition/Copyright: 2ND 99
Publisher: Springer-Verlag New York
Published: 1999
International: No

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Introduction to Mechanics and Symmetry - 2ND 99 edition

ISBN13: 978-0387986432

Jerrold E. Marsden and Tudor S. Ratiu

ISBN13: 978-0387986432
ISBN10: 038798643X
Cover type:
Edition/Copyright: 2ND 99
Publisher: Springer-Verlag New York

Published: 1999
International: No
Summary

Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, especially senior undergraduate and graduate students in mathematics, physics and engineering.

For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line.

Table of Contents

Preface
About the Authors

1 Introduction and Overview
2 Hamiltonian Systems on Linear Symplectic Spaces
3 An Introduction to Infinite-Dimensional Systems
4 Manifolds, Vector Fields, and Differential Forms
5 Hamiltonian Systems on Symplectic Manifolds
6 Cotangent Bundles
7 Lagrangian Mechanics
8 Variational Principles, Constraints, and Rotating Systems
9 An Introduction to Lie Groups
10 Poisson Manifolds
11 Momentum Maps
12 Computation and Properties of Momentum Maps
13 Lie-Poisson and Euler-Poincare Reduction
14 Coadjoint Orbits
15 The Free Rigid Body

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