Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics

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Overview

This advanced text is the first book to describe the subject of classical mechanics in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability.
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Editorial Reviews

From the Publisher
"...a fascinating account of the history and foundations of mechanics... a significant and timely, and indeed personal, contribution to the literature on mechanics, and one which will sit comfortably alongside other definitive Cambridge publications." The Times Higher Education Supplement

"This new book on classical dynamics based on new discoveries in chaos is needed and justified because it is written from a new perspective....A particular merit of this book is its instructive presentation of examples of simple dynamic systems....This is a thought provoking book...[it] can serve as both a textbook for physics and engineering graduate students and a reference or self-study book for physicists, engineers and mathematicians....Serious readers who are interested in chaotic dynamics are advised to read Chaos, Dynamics and Fractal--An Algorithmic Approach to Deterministic Chaos by the same author (Cambridge University Press, 1993)." Journal of Mechanical Engineering Science

"...well written and easy to follow. It provides an excellent physical insight into the modern theory of nonlinear dynamics. This reviewer enjoyed reading this book very much because it clarifies many issues which are presented in an abstract format in other books." Applied Mechanics Reviews

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Product Details

  • ISBN-13: 9780521578820
  • Publisher: Cambridge University Press
  • Publication date: 4/28/2010
  • Edition description: New Edition
  • Pages: 488
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.98 (d)

Table of Contents

Foreword
Acknowledgments
1 Universal laws of nature 1
2 Lagrange's and Hamilton's equations 45
3 Flows in phase space 80
4 Motion in a central potential 126
5 Small oscillations about equilibria 148
6 Integrable and chaotic oscillations 156
7 Parameter-dependent transformations 187
8 Linear transformations, rotations, and rotating frames 204
9 Rigid body motions 223
10 Lagrangian dynamics and transformations in configuration space 247
11 Relativity, geometry, and gravity 262
12 Generalized vs nonholonomic coordinates 295
13 Noncanonical flows 307
14 Damped-driven Newtonian systems 334
15 Hamiltonian dynamics and transformations in phase space 373
16 Integrable canonical flows 409
17 Nonintegrable canonical flows 430
18 Simulations, complexity, and laws of nature 441
Bibliography 453
Index 467
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