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Full Description
Jerry Marsden, one of the world's pre-eminent mechanicians and applied mathematicians, celebrated his 60th birthday in August 2002. The event was marked by a workshop on "Geometry, Mechanics, and Dynamics"at the Fields Institute for Research in the Mathematical Sciences, of which he wasthefoundingDirector. Ratherthanmerelyproduceaconventionalp- ceedings, with relatively brief accounts of research and technical advances presented at the meeting, we wished to acknowledge Jerry's in?uence as a teacher, a propagator of new ideas, and a mentor of young talent. Con- quently, starting in 1999, we sought to collect articles that might be used as entry points by students interested in ?elds that have been shaped by Jerry's work. At the same time we hoped to give experts engrossed in their own technical niches an indication of the wonderful breadth and depth of their subjects as a whole. This book is an outcome of the e?orts of those who accepted our in- tations to contribute. It presents both survey and research articles in the several ?elds that represent the main themes of Jerry's work, including elasticity and analysis, ?uid mechanics, dynamical systems theory, g- metric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread running through this broad tapestry is the use of geometric methods that serve to unify diverse disciplines and bring a widevarietyofscientistsandmathematicianstogether,speakingalanguage which enhances dialogue and encourages cross-fertilization.
Contents
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).
