This is an advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organising principle of the text is integrability vs. nonintegrability. Flows in phase space and transformations are introduced early and systematically and are applied throughout the text. The standard integrable problems of elementary physics are analysed from the standpoint of flows, transformations, and integrability. This approach then allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will be of value to physicists and engineers taking graduate courses in classical mechanics. It will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.
By:
Joseph L. McCauley (University of Houston)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions:
Height: 244mm,
Width: 170mm,
Spine: 25mm
Weight: 770g
ISBN: 9780521578820
ISBN 10: 0521578825
Pages: 488
Publication Date: 07 July 1997
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
Introduction; 1. Universal laws of nature; 2. Lagrange's and Hamilton's equations; 3. Flows in phase space; 4. Motion in a central potential; 5. Small oscillations about equilibria; 6. Integrable and chaotic oscillations; 7. Parameter-dependent transformations; 8. Linear transformations, rotations and rotating frames; 9. Rigid body dynamics; 10. Lagrangian dynamics and transformations in configuration space; 11. Relativity, geometry, and gravity; 12. Generalized vs. nonholonomic coordinates; 13. Noncanonical flows; 14. Damped driven Newtonian systems; 15. Hamiltonian dynamics and transformations in phase space; 16. Integrable canonical flows; 17. Nonintegrable canonical flows; 18. Simulations, complexity, and laws of nature.
Reviews for Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics
'I believe that this book is both a significant and timely, and indeed personal, contribution to the literature on mechanics, and one which will sit comfortably alongside other definitive Cambridge publications.' Nigel Steele, Times Higher Educational Supplement ' ... remarkable imagination and insight ... a godsend to any enterprising and conscientious teacher newly designing a classical mechanics course.' G. Barton, Contemporary Physics 'The book will be valuable to physicists and engineers studying the classical mechanics. It will also be of interest to specialists in nonlinear dynamics, mathematicians, and system theorists.' V. Marinca, Zentralblatt MATH
