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Results tagged with integrable-systems
Search options answers only
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user 2906
2
votes
Accepted
Non-polynomial integrals of motion for polynomial dynamical systems
Here is a tentative Hamiltonian answer having 2 degrees of freedom.
Take $H = (1/2)(1 + a x^2 + bxy + cy^2) (p_x ^2 + p_y ^2)$.
for essentially any parameters $a, b, c$ for which
$ax^2 + bxy + cy …
- 8,336
8
votes
Accepted
Two interacting bodies in an external field
I seriously doubt there is any general criteria. However there are
more than one beautiful explicit examples of an external field which
lead to an integrable problem. The simplest and probably best …
- 8,336
91
votes
What is an integrable system?
I'll take off from the questioner's suggesting that maybe it's better to say what is a NON-integrable system is.
The Newtonian planar three body problem, for most masses, has been proven to be non-in …
- 8,336