Classical mechanics : transformations, flows, integrable, and chaotic dynamics
著者
書誌事項
Classical mechanics : transformations, flows, integrable, and chaotic dynamics
Cambridge University Press, 1997
- : hc.
- : pbk.
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注記
Includes bibliographical references (p. [452]-466) and index
内容説明・目次
内容説明
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.
目次
- 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.
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