All Questions
Tagged with integrable-systems classical-mechanics
7 questions
5
votes
0
answers
241
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A soft question on Gauge Equivalence in Integrable Systems
I have a question about two well-known spectral problems in Integrable Systems. These are the Dirac and the ZS-AKNS spectral problems. They are are known to be gauge equivalent (please see equations (...
- 101
2
votes
0
answers
1k
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Proof of Arnold-Liouville theorem in classical mechanics [closed]
I am currently reading Arnold's book "Mathematical Methods of classical mechanics" on page 278 and I don't see through his arguments there at a point.
Especially, I am talking about the part that ...
- 181
2
votes
0
answers
165
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Nature of separatrix in Fokker--Planck Hamiltonian with two degrees of freedom
Background The semiclassical (weak noise, small $D$) limit of the Fokker--Planck equation
$$\frac{\partial P}{\partial t}=D\frac{\partial^2 P}{\partial x^2}-\frac{\partial}{\partial x}(v(x) P)$$
can ...
- 1,038
4
votes
1
answer
395
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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 ...
- 783
3
votes
0
answers
559
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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 ...
- 197
8
votes
1
answer
432
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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 ...
- 9,720
6
votes
0
answers
450
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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 ...
- 281