Geometry, Mechanics, and Dynamics

by Marsden, Jerrold E.; Holmes, Philip; Weinstein, Alan; Newton, Paul K.

• ISBN13: 9780387955186
• ISBN10: 0387955186
• Format: Hardcover
• Copyright: 2002-09-01
• Publisher: Springer Verlag

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