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Product details:
- Publisher OUP Oxford
- Date of Publication 22 August 2013
- ISBN 9780199673858
- Binding Paperback
- No. of pages788 pages
- Size 239x169x43 mm
- Weight 1278 g
- Language English
- Illustrations 123 line drawings 0
Categories
Short description:
Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a point mass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.
MoreLong description:
Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics, with remarkable applications to many branches of physics (Astronomy, Statistical and Quantum Mechanics, etc.). Rooted in the works of Lagrange, Euler, and Poincaré, it is a classical subject with fascinating developments and still rich with open problems. It addresses such fundamental questions as: Is the solar system stable? Is there a unifying "economy" principle in mechanics? How can a point mass be described as a "wave"?
This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes the challenge to explain the most relevant ideas and to show the most important applications using plain language and "simple" mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book and when more is required, the new mathematical concepts are illustrated, again in plain language. The book is conceived in such a way that some difficult chapters can be bypassed, whilst still grasping the main ideas. However, anybody wishing to go deeper in some directions will find at least the flavour of recent developments and many bibliographical references.
Theory is always accompanied by examples. Many problems are suggested and some are completely worked out at the end of each chapter. The book may effectively be used (and it is in several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.
Pleasantly presented.
Table of Contents:
Geometric and kinematic foundations of Lagrangian mechanics
Dynamics: general laws and the dynamics of a point particle
One-dimensional motion
The dynamics of discrete systems. Lagrangian formalism
Motion in a central field
Rigid bodies: geometry and kinematics
The mechanics of rigid bodies: dynamics
Analytical mechanics: Hamiltonian formalism
Analytical mechanics: variational principles
Analytical mechanics: canonical formalism
Analytical mechanics: Hamilton-Jacobi theory and integrability
Analytical mechanics: canonical perturbation theory
Analytical mechanics: an introduction to ergodic theory and to chaotic motion
Statistical mechanics: kinetic theory
Statistical mechanics: Gibbs sets
Lagrangian formalism in continuum mechanics
Appendices
