Description
Book SynopsisThe approach to classical mechanics adopted in this book includes and stresses recent developments in nonlinear dynamical systems. The concepts necessary to formulate and understand chaotic behavior are presented. Besides the conventional topics (such as oscillators, the Kepler problem, spinning tops and the two centers problem) studied in the frame of Newtonian, Lagrangian, and Hamiltonian mechanics, nonintegrable systems (the Hénon-Heiles system, motion in a Coulomb force field together with a homogeneous magnetic field, the restricted three-body problem) are also discussed. The question of the integrability (of planetary motion, for example) leads finally to the KAM-theorem.This book is the result of lectures on 'Classical Mechanics' as the first part of a basic course in Theoretical Physics. These lectures were given by the author to undergraduate students in their second year at the Johannes Kepler University Linz, Austria. The book is also addressed to lecturers in this field and to physicists who want to obtain a new perspective on classical mechanics.
Table of Contents: The Foundations of Mechanics; One-Dimensional Motion of a Particle; Encountering Peculiar Motion in Two Dimensions; Motion in a Central Force Field; The Gravitational Interaction of Two Bodies; Collisions of Particles. Scattering; Changing the Frame of Reference; Lagrangian Mechanics; Conservation Laws and Symmetries in Many Particle Systems; The Rigid Body; Small Oscillations; Hamilton's Canonical Formulation of Mechanics; Hamilton-Jacobi Theory; From Integrable to Non-Integrable Systems.
