Geometry, Mechanics, and Dynamics,9780387955186

Geometry, Mechanics, and Dynamics

by ; ; ;
ISBN13: 9780387955186
ISBN10: 0387955186
Format: Hardcover
Pub. Date: 2002-09-01
Publisher(s): Springer Verlag
List Price: $89.99

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Summary

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.

Table of Contents

Preface ix
I Elasticity and Analysis 1(110)
Some Open Problems in Elasticity
3(58)
John Ball
Finite Elastoplasticity Lie Groups and Geodesics on SL(d)
61(30)
Alexander Mielke
Asynchronous Variational Integrators
91(20)
Adrian Lew
Michael Ortiz
II Fluid Mechanics 111(130)
Euler--Poincare Dynamics of Perfect Complex Fluids
113(56)
Darryl D. Holm
The Lagrangian Averaged Euler (LAE-α) Equations with Free-Slip or Mixed Boundary Conditions
169(12)
Steve Shkoller
Nearly Inviscid Faraday Waves
181(42)
Edgar Knobloch
Jose M. Vega
The Variational Multiscale Formulation of LES with Application to Turbulent Channel Flows
223(18)
Thomas J. R. Hughes
Assad A. Oberai
III Dynamical Systems 241(86)
Patterns of Oscillation in Coupled Cell Systems
243(44)
Martin Golubitsky
Ian Stewart
Simple Choreographic Motions of N Bodies: A Preliminary Study
287(22)
Alain Chenciner
Joseph Gerver
Richard Montgomery
Carles Simo
On Normal Form Computations
309(18)
Jurgen Scheurle
Sebastian Walcher
IV Geometric Mechanics 327(102)
The Optimal Momentum Map
329(34)
Juan-Pablo Ortega
Tudor S. Ratiu
Combinatorial Formulas for Products of Thom Classes
363(44)
Victor Guillemin
Catalin Zara
Gauge Theory of Small Vibrations in Polyatomic Molecules
407(22)
Robert G. Littlejohn
Kevin A. Mitchell
V Geometric Control 429(32)
Symmetries, Conservation Laws, and Control
431(30)
Anthony M. Bloch
Naomi E. Leonard
VI Relativity and Quantum Mechanics 461(76)
Conformal Volume Collapse of 3-Manifolds and the Reduced Einstein Flow
463(60)
Arthur E. Fischer
Vincent Moncrief
On Quantizing Semisimple Basic Algebras, I: sl(2, R)
523(14)
Mark J. Gotay
VII Jerrold Marsden, 1942-- 537(32)
Curriculum Vitae
539(2)
Some Research Highlights
541(4)
Graduate Students and Post Doctoral Scholars
545(4)
Publications
549(20)
Contributors 569

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