Ebook: Geometry, Mechanics, and Dynamics

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.

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This volume aims to acknowledge J. E. Marsden's influence as a teacher, propagator of new ideas, and mentor of young talent. It presents both survey articles and research articles in the fields that represent the main themes of his work, including elesticity and analysis, fluid mechanics, dynamical systems theory, geometric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread throughout is the use of geometric methods that serve to unify diverse disciplines and bring a wide variety of scientists and mathematicians together in a way that enhances dialogue and encourages cooperation. This book may serve as a guide to rapidly evolving areas as well as a resource both for students who want to work in one of these fields and practitioners who seek a broader view.

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This volume aims to acknowledge J. E. Marsden's influence as a teacher, propagator of new ideas, and mentor of young talent. It presents both survey articles and research articles in the fields that represent the main themes of his work, including elesticity and analysis, fluid mechanics, dynamical systems theory, geometric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread throughout is the use of geometric methods that serve to unify diverse disciplines and bring a wide variety of scientists and mathematicians together in a way that enhances dialogue and encourages cooperation. This book may serve as a guide to rapidly evolving areas as well as a resource both for students who want to work in one of these fields and practitioners who seek a broader view.
Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Some Open Problems in Elasticity....Pages 3-59
Finite Elastoplasticity Lie Groups and Geodesics on SL(d)....Pages 61-90
Asynchronous Variational Integrators....Pages 91-110
Front Matter....Pages 111-111
Euler-Poincar? Dynamics of Perfect Complex Fluids....Pages 169-180
The Lagrangian Averaged Euler (LAE-?) Equations with Free-Slip or Mixed Boundary Conditions....Pages 113-165
Nearly Inviscid Faraday Waves....Pages 181-222
The Variational Multiscale Formulation of LES with Application to Turbulent Channel Flows....Pages 223-239
Front Matter....Pages 241-241
Patterns of Oscillation in Coupled Cell Systems....Pages 243-286
Simple Choreographic Motions of N Bodies: A Preliminary Study....Pages 287-308
On Normal Form Computations....Pages 309-325
Front Matter....Pages 327-327
The Optimal Momentum Map....Pages 329-362
Combinatorial Formulas for Products of Thom Classes....Pages 363-405
Gauge Theory of Small Vibrations in Polyatomic Molecules....Pages 407-428
Front Matter....Pages 429-429
Symmetries, Conservation Laws, and Control....Pages 431-460
Front Matter....Pages 461-461
Conformal Volume Collapse of 3-Manifolds and the Reduced Einstein Flow....Pages 463-522
On Quantizing Semisimple Basic Algebras, I: sl(2, R)....Pages 523-536
Back Matter....Pages 537-571

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This volume aims to acknowledge J. E. Marsden's influence as a teacher, propagator of new ideas, and mentor of young talent. It presents both survey articles and research articles in the fields that represent the main themes of his work, including elesticity and analysis, fluid mechanics, dynamical systems theory, geometric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread throughout is the use of geometric methods that serve to unify diverse disciplines and bring a wide variety of scientists and mathematicians together in a way that enhances dialogue and encourages cooperation. This book may serve as a guide to rapidly evolving areas as well as a resource both for students who want to work in one of these fields and practitioners who seek a broader view.
Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Some Open Problems in Elasticity....Pages 3-59
Finite Elastoplasticity Lie Groups and Geodesics on SL(d)....Pages 61-90
Asynchronous Variational Integrators....Pages 91-110
Front Matter....Pages 111-111
Euler-Poincar? Dynamics of Perfect Complex Fluids....Pages 169-180
The Lagrangian Averaged Euler (LAE-?) Equations with Free-Slip or Mixed Boundary Conditions....Pages 113-165
Nearly Inviscid Faraday Waves....Pages 181-222
The Variational Multiscale Formulation of LES with Application to Turbulent Channel Flows....Pages 223-239
Front Matter....Pages 241-241
Patterns of Oscillation in Coupled Cell Systems....Pages 243-286
Simple Choreographic Motions of N Bodies: A Preliminary Study....Pages 287-308
On Normal Form Computations....Pages 309-325
Front Matter....Pages 327-327
The Optimal Momentum Map....Pages 329-362
Combinatorial Formulas for Products of Thom Classes....Pages 363-405
Gauge Theory of Small Vibrations in Polyatomic Molecules....Pages 407-428
Front Matter....Pages 429-429
Symmetries, Conservation Laws, and Control....Pages 431-460
Front Matter....Pages 461-461
Conformal Volume Collapse of 3-Manifolds and the Reduced Einstein Flow....Pages 463-522
On Quantizing Semisimple Basic Algebras, I: sl(2, R)....Pages 523-536
Back Matter....Pages 537-571
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