Joseph McCauleyCambridge University Press, 5/5/2010EAN 9780521578820, ISBN10: 0521578825Paperback, 488 pages, 24.4 x 17 x 2.5 cmLanguage: EnglishThis 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.Introduction1. Universal laws of nature2. Lagrange's and Hamilton's equations3. Flows in phase space4. Motion in a central potential5. Small oscillations about equilibria6. Integrable and chaotic oscillations7. Parameter-dependent transformations8. Linear transformations, rotations and rotating frames9. Rigid body dynamics10. Lagrangian dynamics and transformations in configuration space11. Relativity, geometry, and gravity12. Generalized vs. nonholonomic coordinates13. Noncanonical flows14. Damped driven Newtonian systems15. Hamiltonian dynamics and transformations in phase space16. Integrable canonical flows17. Nonintegrable canonical flows18. Simulations, complexity, and laws of nature.
