Analytical Mechanics: An Introduction

Paperback | September 1, 2013

byAntonio Fasano, Stefano Marmi

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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 Poincare, it is a classical subject withfascinating 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 originalapproach. 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 variouslevels.

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From the Publisher

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 Poincare, it is a classical subject withfascinating developments and still rich with open ...

Antonio Fasano is Professor in the Department of Mathematics at Universita di Firenze in Italy. Stefano Marmi is Professor at Scuola Normale Superiore in Pisa, Italy. Beatrice Pelloni is Professor in the Department of Mathematics at the University of Reading.
Format:PaperbackDimensions:792 pagesPublished:September 1, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199673853

ISBN - 13:9780199673858

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Table of Contents

1. Geometric and kinematic foundations of Lagrangian mechanics2. Dynamics: general laws and the dynamics of a point particle3. One-dimensional motion4. The dynamics of discrete systems. Lagrangian formalism5. Motion in a central field6. Rigid bodies: geometry and kinematics7. The mechanics of rigid bodies: dynamics8. Analytical mechanics: Hamiltonian formalism9. Analytical mechanics: variational principles10. Analytical mechanics: canonical formalism11. Analytical mechanics: Hamilton-Jacobi theory and integrability12. Analytical mechanics: canonical perturbation theory13. Analytical mechanics: an introduction to ergodic theory and to chaotic motion14. Statistical mechanics: kinetic theory15. Statistical mechanics: Gibbs sets16. Lagrangian formalism in continuum mechanicsAppendices

Editorial Reviews

"Pleasantly presented." --K. Lindsay, University of Glasgow