Global Aspects of Classical Integrable Systems (Paperback)
  • Global Aspects of Classical Integrable Systems (Paperback)
zoom

Global Aspects of Classical Integrable Systems (Paperback)

(author), (author)
£62.99
Paperback 435 Pages / Published: 05/10/2012
  • We can order this

Usually dispatched within 3 weeks

  • This item has been added to your basket
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.

Publisher: Springer Basel
ISBN: 9783034898171
Number of pages: 435
Weight: 694 g
Dimensions: 235 x 155 x 23 mm
Edition: Softcover reprint of the original 1st ed. 199


MEDIA REVIEWS

"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

You may also be interested in...

A Student's Guide to Waves
Added to basket
Inside Interesting Integrals
Added to basket
Tensor Calculus for Physics
Added to basket
Schroedinger Operators
Added to basket
Partial Differential Equations
Added to basket
Measurements and their Uncertainties
Added to basket
Group Theory
Added to basket
£59.99
Hardback
The Language of Physics
Added to basket
Quantum Mathematical Physics
Added to basket
Physical Mathematics
Added to basket
Einstein's Physics
Added to basket
£32.99
Hardback
Riemannian Geometry and Geometric Analysis
Added to basket
The Physics of Quantum Mechanics
Added to basket

Reviews

Please sign in to write a review

Your review has been submitted successfully.