Lectures on Mechanics

by Jerrold E. Marsden

Overview

The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule.

Product Details

ISBN-13:	9780521428446
Publisher:	Cambridge University Press
Publication date:	04/30/1992
Series:	London Mathematical Society Lecture Note Series , #174
Pages:	268
Product dimensions:	5.98(w) x 9.02(h) x 0.59(d)

Table of Contents

1. Introduction; 2. A crash course in geometric mechanics; 3. Cotangent bundle reduction; 4. Relative equilibria; 5. The energy-momentum method; 6. Geometric phases; 7. Stabilization and control; 8. Discrete reduction; 9. Mechanical integrators; 10. Hamiltonian bifurcations; References.

Editorial Reviews

"...centres around symmetry and symplectic quotients. Many examples are given illustrating the utility and relevance of symplectic quotients....readable and stimulating." Michael Atiyah, Bulletin of the American Mathematical Society

"...The virtue [of this book] is in the breadth, relevance, and complexity of the examples treated..." Mathematical Reviews

From the Publisher