Advanced Mechanics

Description

This book can be used as a textbook for a graduate course on mechanics or for self-study. There are a variety of problems ranging from exercises that verify parts of the text, moderately difficult calculations, to suggested research projects. Connections to other disciplines of mathematics and physics are emphasized.

• Connects modern ideas on chaos to ancient questions of mechanics
• Numerical examples help in understanding abstract results
• Connections to quantum mechanics, relativity, and optics
• Self-contained introduction to Riemannian geometry
• Detailed study of the Three Body problem
• KAM theory introduced using Newton's iteration

About the Author(s)

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

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).

Table of Contents

1:The Variational Principle
2:Conservation Laws
3:The Simple Pendulum
4:The Kepler Problem
5:The Rigid Body
6:Geometric Theory of Ordinary Differential Equations
7:Hamilton's Principle
8:Geodesics
9:Hamilton-Jacobi Theory
10:Integrable Systems
11:The Three Body Problem
12:The Restricted Three Body Problem
13:Magnetic Fields
14:Poisson and Symplectic Manifolds
15:Discrete Time
16:Dynamics in One Real Variable
17:Dynamics On The Complex Plane
18:KAM Theory

Reviews

"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

"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

"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

"The book is elegant, concise, enjoyable and sprinkled with illuminating examples." - Peter MacGregor, The Mathematical Gazette