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Park City Lectures on Mechanics, Dynamics, and Symmetry

Marsden, Jerrold E. (1999) Park City Lectures on Mechanics, Dynamics, and Symmetry. In: Symplectic geometry and topology. IAS/Park City Mathematics series. No.7. American Mathematical Society , pp. 335-430. ISBN 0821808389.

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In these ve lectures, I cover selected items from the following topics: 1. Reduction theory for mechanical systems with symmetry, 2. Stability, bifurcation and underwater vehicle dynamics, 3. Systems with rolling constraints and locomotion, 4. Optimal control and stabilization of balance systems, 5. Variational integrators. Each topic itself could be expanded into several lectures, but I limited myself to what I could reasonably explain in the allotted time. The hope is that the overview is informative enough so that the reader can understand the fundamental ideas and can intelligently choose from the literature for additional details on topics of interest. Compatible with the theme of the PCI graduate school, I assume that the readers are familiar with the elements of geometric mechanics, including the basics of symplectic and Poisson geometry. The reader can find the needed background in, for example, Marsden and Ratiu [1998].

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Additional Information:© 1999, AMS. July 17, 1997, this version: January 18, 1998. These lectures present a survey of some of the topics done in collaboration with many coauthors over the last few years. Specific reference is made directly in the text, but I am very grateful for their rewarding collaboration. The organizers, staff and participants at the Park City Institute are to be congratulated for producing a stimulating and productive event. I would also like to thank the University of California, Berkeley, the California Institute of Technology and the National Science Foundation for helping support my research over the years. Pasadena, CA January, 1998.
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University of California, BerkeleyUNSPECIFIED
California Institute of TechnologyUNSPECIFIED
Series Name:IAS/Park City Mathematics series
Issue or Number:7
Record Number:CaltechAUTHORS:20100831-082140722
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19727
Deposited By: Ruth Sustaita
Deposited On:01 Sep 2010 19:41
Last Modified:03 Oct 2019 02:00

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