3
votes
0answers
38 views

Weinstein's local classification of Lagrangian foliations

In the paper "Symplectic manifolds and their Lagrangian submanifolds", Weinstein showed that locally all the Lagrangian foliations are symplectomorhic to the fiber foliation of a cotangent bundle. I ...
3
votes
0answers
507 views

Find a second integral for Arnold's example

Consider Arnold's example for Arnold diffusion 1964. $$H=I_1^2/2+I_2^2/2+\epsilon(1-\cos\theta_2)(1+\mu(\sin\theta_1+\sin t)) $$ We can first make it a system of three degrees of freedom. Then we ...
7
votes
1answer
373 views

Two interacting bodies in an external field

Hope, MO is the right place for this question (if not so: where would you pose it?). Consider a two-body system in classical mechanics. As long as the interaction depends only on the distance of the ...
5
votes
0answers
402 views

Differential equation of line tangent to caustics

This problem (or rather, statement that I cannot understand) has arisen in a paper I have been reading "Geometry of Integrable Billiards and Pencils of Quadrics" by Dragovic and Radnovic. I'd be most ...