**Fields Institute Communications**

Volume: 7;
1996;
260 pp;
Hardcover

MSC: Primary 70;

Print ISBN: 978-0-8218-0261-8

Product Code: FIC/7

List Price: $114.00

Individual Member Price: $91.20

**Electronic ISBN: 978-1-4704-2975-1
Product Code: FIC/7.E**

List Price: $114.00

Individual Member Price: $91.20

# Mechanics Day

Share this page *Edited by *
*William F. Shadwick; Perinkulam Sambamurthy Krishnaprasad; Tudor S Ratiu*

A co-publication of the AMS and Fields Institute

This volume presents the proceedings of a workshop held at The Fields Institute in June 1992 both as a commemoration of the 25th anniversary of the publication of “Foundations of Mechanics” by Ralph Abraham and Jerrold Marsden and as a celebration of Marsden's 50th birthday. The publication of that first edition marked a period of remarkable resurgence in all aspects of mechanics, which has continued through the publication of the second edition in 1978, deeply nourished by contacts with a variety of areas of mathematics, including topology, differential geometry, Lie theory, and partial differential equations. The papers collected in this volume reflect these fruitful ties as well as some others, strengthened over the last two decades, with areas of applied science including control theory.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Mechanics Day

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Experimental mechanics, the first forty years 110
- On the infinitesimal geometry of integrable systems 514
- The toda PDE and the geometry of the diffeomorphism group of the annulus 5766
- Separation of rotations of coupled gyrostats 93102
- A theory of cosmological models 107116
- Loop algebra moment maps and Hamiltonian models for the Painleve transcendants 155164
- The planar filament equation 171180
- The localized induction equation, the Heisenberg chain, and the nonlinear Schrodinger equation 181190
- The Griffiths-Bryant algorithm and the Dirac theory of constraints 189198
- Lagrangian mechanics and groupoids 207216
- Optimal control of a rigid body with two oscillators 233242
- Back Cover Back Cover1271

#### Readership

Research mathematicians and engineers.