A Modern Approach to Classical Mechanics

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World Scientific, Jan 1, 2002 - Science - 442 pages
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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.

  

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two fixed cnetres!!

Contents

Introduction
1
The foundations of mechanics
11
Onedimensional motion of a particle
27
Encountering peculiar motion in two dimensions
59
Motion in a central force field
85
The gravitational interaction of two bodies
119
Collisions of particles Scattering
145
Changing the frame of reference
167
The rigid body
249
Small oscillations
291
Hamiltons canonical formulation of mechanics
317
HamiltonJacobi theory
347
From integrable to nonintegrable systems
381
In retrospect
411
B Rotations and tensors
421
Index
437

Lagrangian mechanics
191
Conservation laws and symmetries in many particle
225

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