Analytical Mechanics

Antonio Fasano, Stefano Marmi - Collection Oxford Graduate Texts

774 pages, parution le 06/04/2006

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Résumé

Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics. Rooted in the works of Lagrange, Euler, Poincaré (to mention just a few), it is a very classical subject with fascinating developments and still rich of 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'? And has remarkable applications to many branches of physics (Astronomy, Statistical Mechanics, Quantum Mechanics).

This book was written to fill a gap between elementary expositions and more advanced (and clearly more stimulating) material. It takes up the challenge to explain the most relevant ideas (generally highly non-trivial) and to show the most important applications using a plain language and 'simple' mathematics, often through an original approach. Basic calculus is enough for the reader to proceed through the book. New mathematical concepts are fully introduced and illustrated in a simple, student-friendly language. More advanced chapters can be omitted while still following the main ideas. Anybody wishing to go deeper in some direction will find at least the flavour of recent developments and many bibliographical references.

The 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 has been used at several Italian Universities) for undergraduate as well as for PhD courses in Physics and Mathematics at various levels.

Sommaire

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
Langrangian Formalism in Continuum Mechanics
Appendices

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Antonio Fasano, Stefano Marmi
Collection	Oxford Graduate Texts
Parution	06/04/2006
Nb. de pages	774
Format	17 x 25
Couverture	Relié
Poids	1409g
Intérieur	Noir et Blanc
EAN13	9780198508021
ISBN13	978-0-19-850802-1