ean 9780199673858 temática MATEMÁTICAS año Publicación 2013 idioma INGLÉS editorial OXFORD UNIVERSITY PRESS formato RÚSTICA 42,35 €    PEDIR   NOVEDAD

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Illustrates the basic material, as well as some of the deepest and most advanced concepts in plain language and with simple mathematical tools. Presents core of Analytical Mechanics, and some of its most relevant applications e.g. to Astronomy, Statistical Mechanics, Continuum Mechanics. Readership of graduate students in theoretical physics, mechanical engineering, and applied mathematics. Contains many problems throughout the book, as well as a section of solutions attached to each chapter. Only prerequisite is basic calculus. Advanced mathematics is explained in a simple, student-friendly style. 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. Readership: Advanced undergraduate and graduate students of applied mathematics, theoretical physics, and mechanical engineering.

indíce

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: Lagrangian formalism in continuum mechanics Appendices