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.
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"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
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
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XVI, 435 Seiten, Fadenheftung, Format 16,5 x 23,6 cm, hartgebundener u. mattkaschierter Original-Pappband. * Zweite ISBN-Nr.: 0-8176-5485-2. Bibliography + Index auf den Seiten 411-435. Erhaltung: Keine Mängel, insgesamt ein sehr gutes und frisches Exemplar [Eine größere Sammlung Physik, Mathematik, Astronomie und verwandte Gebiete wird derzeit in den Bestand eingearbeitet. Sie finden diese Titel bei uns in den gleichnamigen Rubriken]. Sprache: Englisch. Artikel-Nr. 28683
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Zustand: Fine. 435 pp., hardcover, tips lightly rubbed, else fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Artikel-Nr. ZB1310571
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Zustand: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. Clean from markings. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,1000grams, ISBN:9783764354855. Artikel-Nr. 9927357
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Hardback. Zustand: As New. xvi 435p large sturdy textbook, smooth sky-blue cover with white lettering and designs, like new condition, little to no wear, firm binding, clear and sharp text, no highlighting or annotations, a very good copy Language: English Weight (g): 818. Artikel-Nr. 233454
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Zustand: Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,1000grams, ISBN:9783764354855. Artikel-Nr. 9647521
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