Theory of Orbits : Volume 1: Integrable Systems and Non-perturbative Methods

Abstract

This textbook treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motions. The book is meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry. The first volume begins with classical mechanics and with a thorough treatment of the 2-body problem, including regularization, followed by an introduction to the N-body problem with particular attention given to the virial theorem. Then the authors discuss all important non-perturbative aspects of the 3-body problem. They end with a final chapter on integrability of Hamilton-Jacobi systems and the search for constants of motion. Introduction -- The Theory of Orbits from Epicycles to "Chaos" -- 1. Dynamics and Dynamical Systems -- Quod Satis -- 2. The Two-Body Problem -- 3. The N-Body Problem -- 4. The Three-Body Problem -- 5. Orbits in Given Potentials -- Mathematical Appendix -- Bibliographical Notes -- Name Index -- Subject Index.