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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. Many mathematicians have established a modern view of the role played by algebraic geometry in recent years. This book presents some of these modern 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, while in appendices the author describes general, abstract theory. She gives the methods a topological application, for the first time in book form, to the study of Liouville tori and their bifurcations.Read more
- Was the first book making the subject accessible to graduate students
- Suited for both pure and applied audiences as lots of examples
- Well-known author (has written related books before)
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"Among its virtues, this book strikes me as a marvelous introduction for students....the book is peppered with wisdom, the things that books never tell you..." Mathematical Reviews
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- Date Published: November 1999
- format: Paperback
- isbn: 9780521779197
- length: 148 pages
- dimensions: 228 x 153 x 8 mm
- weight: 0.215kg
- contains: 35 b/w illus.
- availability: Available
Table of Contents
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
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