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Re: Poincare section for double pendulum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120664] Re: Poincare section for double pendulum
  • From: JUN <noeckel at gmail.com>
  • Date: Wed, 3 Aug 2011 07:05:22 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j10l10$osi$1@smc.vnet.net>

On Jul 30, 3:05 am, "Christoph Lhotka" <christoph.lho... at univie.ac.at>
wrote:
> Hello,
>
> this is just a starting point...
>
> Try to solve your problem with the method "EventLocator" in NDSolve to
> limit your output to values on the Poincar=E9 surface of section.
> You could use e.g. FindInstance to get a good set of initial conditions
> for given energy value of the Hamiltonian.
>
> Good luck,
>
> Christoph

Yes, the chapter
tutorial/NDSolveEventLocator
in the help browser is definitely worth reading (in particular the
section about the Henon-Heiles system)!
My simpler approach could give you duplicate zeros of x[t] -- which
doesn't matter for the Poincare section (and could be fixed by
DeleteDuplicates). However, EventLocator is a cleaner solution.

Jens





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