A Modern Approach to Classical Mechanics
The approach to classical mechanics adopted in this book includes recent developments in nonlinear dynamical systems, and 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 Henon -- Heiles system, the Coulomb force and the 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.
The foundations of mechanics
Onedimensional 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
The rigid body
Hamiltons canonical formulation of mechanics
From integrable to nonintegrable systems
B Rotations and tensors
Conservation laws and symmetries in many particle