Analytical Mechanics: An Introduction

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Antonio Fasano (Dipartimento di Matematica, Universita di Firenze) Stefano Marmi (Scuola Normale Superiore, Pisa)

Analytical Mechanics

An Introduction

Antonio Fasano (Dipartimento di Matematica, Universita di Firenze), Stefano Marmi (Scuola Normale Superiore, Pisa), Beatrice Pelloni (Department of Mathematics, University of Reading)

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English

Oxford University Press
01 April 2006

Applied mathematics; Analytical mechanics; Fluid mechanics; Mechanical engineering

Series: Oxford Graduate Texts

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.

By: Antonio Fasano (Dipartimento di Matematica Universita di Firenze), Stefano Marmi (Scuola Normale Superiore, Pisa)
Translated by: Beatrice Pelloni (Department of Mathematics University of Reading)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 248mm, Width: 174mm, Spine: 45mm
Weight: 1.512kg
ISBN: 9780198508021
ISBN 10: 0198508026
Series: Oxford Graduate Texts
Pages: 788
Publication Date: 01 April 2006
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

1: Geometric and Kinematic Foundations of Lagrangian Mechanics 2: Dynamics: General Laws and the Dynamics of a Point Particle 3: One-dimensional Motion 4: The Dynamics of Discrete Systems. Lagrangian Formalism 5: Motion in a Central Field 6: Rigid Bodies: Geometry and Kinematics 7: The Mechanics of Rigid Bodies: Dynamics 8: Analytical Mechanics: Hamiltonian Formalism 9: Analytical Mechanics: Variational Principles 10: Analytical Mechanics: Canonical Formalism 11: Analytical Mechanics: Hamilton-Jacobi Theory and Integrability 12: Analytical Mechanics: Canonical Perturbation Theory 13: Analytical Mechanics: An Introduction to Ergodic Theory and to Chaotic Motion 14: Statistical Mechanics: Kinetic Theory 15: Statistical Mechanics: Gibbs Sets 16: langrangian Formalism in Continuum Mechanics Appendices

"Professor Antonio Fasano Dipartimento di Matematica ""U. Dini"" Universita di Firenze Viale Morgagni 67A 50134 Firenze Italy Professor Stefano Marmi Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa Italy"