Spinning Tops
A Course on Integrable Systems

Graduate text looking at interaction of algebraic geometry and classical mechanics.

M. Audin (Author)

9780521779197, Cambridge University Press

Paperback, published 13 November 1999

148 pages, 35 b/w illus.
22.8 x 15.3 x 0.8 cm, 0.215 kg

'This book has several remarkable features … This small book has very rich contents which can be commended to any mathematician or physicist interested in the subject.' European Mathematical Society

Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.

Introduction
1. The rigid body with a fixed point
2. The symmetric spinning top
3. The Kowalevski top
4. The free rigid body
5. Non-compact levels: a Toda lattice
Appendix 1. A Poisson structure on the dual of a Lie algebra
Appendix 2. R-matrices and the 'AKS theorem'
Appendix 3. The eigenvector mapping and linearising flows
Appendix 4. Complex curves, real curves and their Jacobians
Appendix 5. Prym varieties
Bibliography
Index.

Subject Areas: Classical mechanics [PHD], Applied mathematics [PBW], Calculus & mathematical analysis [PBK]