文档介绍：Park City Lectures on Mechanics,
Dynamics, and Symmetry
Jerrold E. Marsden
July 17, 1997, this version: January 18, 1998
Contents
Preface iv
1 Reduction for Mechanical Systems with Symmetry 1
2 Stability, Underwater Vehicle Dynamics and Phases 13
3 Systems with Rolling Constraints and otion 31
4 Optimal Control and Stabilization of Balance Systems 43
5 Variational Integrators 53
i
Preface
In these five 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 otion,
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].
Acknowledgments. These lectures present a survey of some of the topics done in col-
laboration 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.
anizers, 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 Jerrold E. Marsden
January, 1998
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