IAS/Park City Mathematics Series
Volume 7, 1999Park City Lectures on Mechanics,
Dynamics, and Symmetry
Jerrold E. Marsden
Introduction
In these five lectures, I cover selected items from the following topics:l. Reduction theory for mechanical systems with symmetry,
- Stability, bifurcation and underwater vehicle dyna mics,
- Systems with rolling constraints and locomotion,
- Optimal control and stabilization of balance systems,
- 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].
Acknowledgments. 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.
(^1) Control and Dynamical Systems 107 - 81 , Caltech, Pasadena, CA 91125.
E-mail address: marsden©cds. cal tech. edu.
@ 1999 A m erican Mathe matical Socie t y
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