Lectures On Mechanics by Jerrold E. MarsdenLectures On Mechanics by Jerrold E. Marsden

Lectures On Mechanics

byJerrold E. Marsden

Paperback | May 29, 1992

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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.
Title:Lectures On MechanicsFormat:PaperbackDimensions:268 pages, 8.98 × 5.98 × 0.59 inPublished:May 29, 1992Publisher:Cambridge University Press

The following ISBNs are associated with this title:

ISBN - 10:0521428440

ISBN - 13:9780521428446

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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.

From Our Editors

The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and 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, studies using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems.

Editorial Reviews

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