Convexity Methods in Hamiltonian Mechanics

Released on by Ivar Ekeland
preview-18

  • Convexity Methods in Hamiltonian Mechanics Book Detail

  • Author : Ivar Ekeland
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 258
  • ISBN 13 : 3642743315
  • File Size : 7,7 MB
DOWNLOAD BOOK

Convexity Methods in Hamiltonian Mechanics by Ivar Ekeland PDF Summary

Book Description: 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.

Disclaimer: www.yourbookbest.com does not own Convexity Methods in Hamiltonian Mechanics books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Convexity Methods in Hamiltonian Mechanics

Convexity Methods in Hamiltonian Mechanics

File Size : 85,85 MB
Total View : 979 Views
DOWNLOAD

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial

Progress in Nonlinear Analysis

Progress in Nonlinear Analysis

File Size : 97,97 MB
Total View : 3126 Views
DOWNLOAD

The real world is complicated, as a result of which most mathematical models arising from mechanics, physics, chemistry and biology are nonlinear. Based on the

Calculus Without Derivatives

Calculus Without Derivatives

File Size : 7,7 MB
Total View : 3780 Views
DOWNLOAD

Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usu

Néron Models

Néron Models

File Size : 85,85 MB
Total View : 590 Views
DOWNLOAD

Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithm