In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter in the problem, the mass of the perturbing body for instance, and for = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the ...
Read More
In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter in the problem, the mass of the perturbing body for instance, and for = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L =l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods."
Read Less
Add this copy of Convexity Methods in Hamiltonian Mechanics.; to cart. $9.00, good condition, Sold by J. Hood, Booksellers, Inc. rated 5.0 out of 5 stars, ships from Baldwin City, KS, UNITED STATES, published 1990 by Springer.
Add this copy of Convexity Methods in Hamiltonian Mechanics to cart. $51.64, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2011 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Trade paperback (US). Glued binding. 247 p. Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /, 19. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Convexity Methods in Hamiltonian Mechanics to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2011 by Springer.
Add this copy of Convexity Methods in Hamiltonian Mechanics to cart. $58.78, new condition, Sold by booksXpress, ships from Bayonne, NJ, UNITED STATES, published 2011 by Springer.
