Geometry, Mechanics, and Dynamics: Volume in Honor of the 60th Birthday of J. E. Marsden

ISBN-13: 9781441930347 / Angielski / Miękka / 2011 / 571 str.

Paul Newton; Phil Holmes; Alan Weinstein

Opis

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.

Recenzje

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)

Spis treści

I Elasticity and Analysis * Some Open Problems * Finite Elastoplasticity Lie Groups and Geodesics on SL *Asynchronous Variational Integrators * II Fluid Mechanics * Euler-Poincare' Dynamics of Perfect Complex Fluids * The Lagrangian Averaged Euler Equations with Free-Slip or Mixed Boundary Conditions * Nearly Inviscid Faraday Waves * The Variational Multiscale Formulation of LES with Application to Turbulent Channel Flows * III Dynamical Systems * Patterns of Oscillation in Coupled Cell Systems * Simple Choreographic Motions of N Bodies: A Preliminary Study * On Normal Form Computations * IV Geometric Mechanics * The Optimal Momentum Map * Combinatorial Formulas for Products of Thom Classes * Gauge Theory of Small Vibrations in Polyatomic Molecules * V 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 * VII Jerrold Marsden, 1942- * Curriculum Vitae * Some Research Highlights * Graduate Students and Post Doctoral Scholars * Publications * Contributors

O autorze

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.