Geometry, Mechanics, and Dynamics

The common thread running throughout this volume is the use of geometric methods that serve to unify diverse disciplines and bring together a variety of scientists and mathematicians, in a manner that encourages cross-fertilization. Professor J.E. Marsden is a unique figure in this regard as his work has significantly influenced three distinctly separate communities of mathematicians, physicists, and engineers.

From the reviews: "Geometric Mechanics (GM) is a basic way of thinking . most of the papers are very accessible with long introductions and good surveys of other contributions. Finally, the volume is typeset so beautifully in a unified format, that it is satisfying to hold the book and pleasing to look at the articles, as well as to read them. The volume is worth serious study, and it was well worth the long wait ." (Darryl Holm, UK Nonlinear News, March, 2003)

Inhalt
Elasticity and Analysis.- Some Open Problems in Elasticity.- Finite Elastoplasticity Lie Groups and Geodesics on SL(d).- Asynchronous Variational Integrators.- Fluid Mechanics.- Euler-Poincaré Dynamics of Perfect Complex Fluids.- The Lagrangian Averaged Euler (LAE-?) Equations with Free-Slip or Mixed Boundary Conditions.- Nearly Inviscid Faraday Waves.- The Variational Multiscale Formulation of LES with Application to Turbulent Channel Flows.- Dynamical Systems.- Patterns of Oscillation in Coupled Cell Systems.- Simple Choreographic Motions of N Bodies: A Preliminary Study.- On Normal Form Computations.- Geometric Mechanics.- The Optimal Momentum Map.- Combinatorial Formulas for Products of Thom Classes.- Gauge Theory of Small Vibrations in Polyatomic Molecules.- Geometric Control.- Symmetries, Conservation Laws, and Control.- Relativity and Quantum Mechanics.- Conformal Volume Collapse of 3-Manifolds and the Reduced Einstein Flow.- On Quantizing Semisimple Basic Algebras, I: sl(2, R).

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