Classical Mechanics Transformations, Flows, Integrable and Chaotic Dynamics [Hardcover]

An advanced 1997 text for first-year graduate students in physics and engineering taking a standard classical mechanics course.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.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.An advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course, this is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability. It introduces flows in phase space and transformations early and illustrates their applications throughout the text. The standard integrable problems of elementary physics are analyzed from the standpoint of flows, transformations, and integrability. This approach 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 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 sylC.