Advanced Mechanics

From Euler's Determinism to Arnold's Chaos

S. G. Rajeev (Department of Physics and Astronomy, University of Rochester)

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English

Oxford University Press
22 August 2013

Mathematics & Sciences; Applied mathematics; Classical mechanics; Quantum physics (quantum mechanics & quantum field theory); Mathematical physics

"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 to re-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 Schrödinger 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 (the original 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 unified theory of optics and mechanics; how Riemannian reometry 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 Trojan asteroids; 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."

By: S. G. Rajeev (Department of Physics and Astronomy University of Rochester)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 245mm, Width: 174mm, Spine: 11mm
Weight: 328g
ISBN: 9780199670864
ISBN 10: 0199670862
Pages: 184
Publication Date: 22 August 2013
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Paperback
Publisher's Status: Active

Prof. 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. He was promoted to Associate Professor in 1993 and to Professor in 2000. Prof. Rajeev has held visiting appointments at the Institute for Advanced Study, Princeton (1991), the Research Institute for Theoretical Physics, Helsinki (1991), and the Mittag-Leffler Institute, Stockholm (1998).

Reviews for Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

The book is elegant, concise, enjoyable and sprinkled with illuminating examples. * Peter MacGregor, The Mathematical Gazette * Rajeev approaches his choice of topics and organization from the point of view of one who is intimately familiar with modern physics. Although he starts from very elementary classical mechanics, he nevertheless does not shy away from sophisticated mathematical tools, such as elliptic functions, which he develops from scratch. This book should be of interest to many physics graduate students and researchers in physics, as well as to many mathematicians. * Leonard Gross, Cornell University * Sarada Rajeev has produced a masterpiece which is as steeped in tradition as it is modern in outlook. The book is a minimalist's dream, unleashing on the unsuspecting reader a treasure trove of novel results within its slender frame. The informal yet stimulating narrative, the excellent choice of topics, and the lucid explanations truly make the book a connoisseur's delight. * V. V. Sreedhar, Chennai Mathematical Institute * The book appears to be well suited to serve the intended role of introducing physics students to mechanics and making clear to them the relevance of the subject for modern physics; but it will also be useful to mathematics students to understand that the subject is relevant and alive well beyond the classical realms of applications and/or abstract mathematical developments. * Giuseppe Gaeta, Zentralblatt Math *