Advanced Mechanics: From Eulers Determinism to Arnolds Chaos

Paperback | September 11, 2013

byS. G. Rajeev

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Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need tore-evaluate the purpose of learning mechanics and look at old material in the light of modern developments.Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrodinger equation, hydrogen atom) it is time to go back and relearn classical mechanics in greater depth. It is the intent of this book to take you through the ancient (theoriginal meaning of "classical") parts of the subject quickly: the ideas started by Euler and ending roughly with Poincare. We then take up the developments of twentieth century physics that have largely to do with chaos and discrete time evolution (the basis of numerical solutions). Along the way you will learn about elliptic functions and their connection to the Arithmetico-Geometric-Mean; Einstein's calculation of the perihelion shift of Mercury; that spin is really a classical phenomenon; how Hamilton came very close to guessing wave mechanics when he developed a unifiedtheory of optics and mechanics; how Riemannian geometry is useful to understand the impossibility of long range weather prediction; why the maximum of the potential is a stable point of equilibrium in certain situations; the similarity of the orbits of particles in atomic traps and of the Trojanasteroids; about Julia sets and the Mandelblot; what Feigenbaum constants are and how Newton's iterations help establish the Kolmogorov-Arnold-Moser theorem. By the end you should be ready to absorb modern research in mechanics.

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Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need tore-evaluate the purpose of learning mechanics a...

Professor Rajeev received his B.Sc. in Physics from the University of Kerala, Trivandrum, India (1979), and his Ph.D. in Physics from Syracuse University (1984). He was a postdoctoral fellow at the Massachusetts Institute of Technology (1984-87) before joining the University of Rochester as an Assistant Professor of Physics in 1987. H...

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Format:PaperbackDimensions:176 pages, 9.69 × 6.73 × 0.68 inPublished:September 11, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199670862

ISBN - 13:9780199670864

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Table of Contents

1. The Variational Principle2. Conservation Laws3. The Simple Pendulum4. The Kepler Problem5. The Rigid Body6. Geometric Theory of Ordinary Differential Equations7. Hamilton's Principle8. Geodesics9. Hamilton-Jacobi Theory10. Integrable Systems11. The Three Body Problem12. The Restricted Three Body Problem13. Magnetic Fields14. Poisson and Symplectic Manifolds15. Discrete Time16. Dynamics in One Real Variable17. Dynamics On The Complex Plane18. KAM Theory

Editorial Reviews

"Rajeev's book provides a fresh look at the venerable subject of Classical Mechanics. Mathematical results on integrability, geodesic flows and the three-body problem, usually left out of physics textbooks, are introduced in a compact and elegant way and connected to recent developments onchaotic dynamics. Instructors will enjoy it as a textbook for an advanced Classical Mechanics course or as a complement to a more basic textbook in an introductory graduate course." --Yannick Meurice, The University of Iowa