Classical mechanics : transformations, flows, integrable, and chaotic dynamics

Joseph L. McCauley

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[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.

「Nielsen BookData」より

[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.

「Nielsen BookData」より

この本の情報

書名 Classical mechanics : transformations, flows, integrable, and chaotic dynamics
著作者等 McCauley, Joseph L.
出版元 Cambridge University Press
刊行年月 1997
ページ数 xvii, 469 p.
大きさ 25 cm
ISBN 0521578825
0521481325
NCID BA30084535
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言語 英語
出版国 イギリス
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