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Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics

Classical Mechanics: Transformations, Flows, Integrable and Chaotic Dynamics

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Joseph McCauley
Cambridge University Press, 5/5/2010
EAN 9780521578820, ISBN10: 0521578825

Paperback, 488 pages, 24.4 x 17 x 2.5 cm
Language: English

This is an advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course. It was 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.

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.