| Lectures on Mechanics Contributor(s): Marsden, Jerrold E. (Author), Cassels, J. W. S. (Editor), Hitchin, N. J. (Editor) |
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ISBN: 0521428440 ISBN-13: 9780521428446 Publisher: Cambridge University Press OUR PRICE: $83.59 Product Type: Paperback - Other Formats Published: May 1992 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Science | Mechanics - General - Science | Physics - Mathematical & Computational - Mathematics | Applied |
| Dewey: 531.015 |
| LCCN: 93104026 |
| Series: London Mathematical Society Lecture Notes |
| Physical Information: 0.71" H x 6.12" W x 9.02" (0.91 lbs) 268 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |