Synopsis
This book gives a complete global geometric description of the motion of the two di mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary? The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions to making local action angle coordinates global such as monodromy were not known when these works were written.
"synopsis" may belong to another edition of this title.
Review
"Ideal for someone who needs a thorough global understanding of one of these systems [and] who would like to learn some of the tools and language of modern geometric mechanics. The exercises at the end of each chapter are excellent. The book could serve as a good supplementary text for a graduate course in geometric mechanics."
--SIAM Review
"About this title" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Global Aspects of Classical Integrable Systems
Stock Image
Global Aspects of Classical Integrable Systems
Seller: Lucky's Textbooks, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # ABLIING23Mar3113020039014
Stock Image
Global Aspects of Classical Integrable Systems
Seller: California Books, Miami, FL, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # I-9783034898171
Stock Image
Global Aspects of Classical Integrable Systems
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9783034898171_new
Buy New
US$ 66.45
Shipping:
US$ 15.73
From United Kingdom to U.S.A.
Quantity: Over 20 available
Seller Image
Global Aspects of Classical Integrable Systems
Published by
Birkhäuser Basel Okt 2012, 2012
ISBN 10: 3034898177
ISBN 13: 9783034898171
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book gives a complete global geometric description of the motion of the two di mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions to making local action angle coordinates global such as monodromy were not known when these works were written. 456 pp. Englisch. Seller Inventory # 9783034898171
Stock Image
Global Aspects of Classical Integrable Systems
Seller: Books Puddle, New York, NY, U.S.A.
Seller rating 4 out of 5 stars
Condition: New. pp. 458. Seller Inventory # 2698253576
Stock Image
Global Aspects of Classical Integrable Systems
Print on DemandSeller: Majestic Books, Hounslow, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. Print on Demand pp. 458 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam. Seller Inventory # 95192279
Buy New
US$ 88.99
Shipping:
US$ 8.54
From United Kingdom to U.S.A.
Quantity: 4 available
Stock Image
Global Aspects of Classical Integrable Systems
Print on DemandSeller: Biblios, Frankfurt am main, HESSE, Germany
Seller rating 5 out of 5 stars
Condition: New. PRINT ON DEMAND pp. 458 Acknowledgements. Seller Inventory # 1898253570
Seller Image
Global Aspects of Classical Integrable Systems
Seller: moluna, Greven, Germany
Seller rating 4 out of 5 stars
Condition: New. Seller Inventory # 4319624
Buy New
US$ 57.43
Shipping:
US$ 56.47
From Germany to U.S.A.
Quantity: Over 20 available
Seller Image
Global Aspects of Classical Integrable Systems
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book gives a complete global geometric description of the motion of the two di mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions to making local action angle coordinates global such as monodromy were not known when these works were written. Seller Inventory # 9783034898171
Seller Image
Global Aspects of Classical Integrable Systems
Seller: preigu, Osnabrück, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Global Aspects of Classical Integrable Systems | Richard H. Cushman (u. a.) | Taschenbuch | xvi | Englisch | 2012 | Birkhäuser | EAN 9783034898171 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 105706131