Re: Poincare sections

• To: mathgroup at smc.vnet.net
• Subject: [mg37335] Re: Poincare sections
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 24 Oct 2002 02:55:20 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <200210210630.CAA12321@smc.vnet.net> <ap5asb\$3un\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

that work only for non-autonomos systems but the original
message speak about Hamiltonian systems. For a
autonomous system your function does not work at all, because
you have to find the intersection points of the solution
with a plane in phase space.

Regards
Jens

Selwyn Hollis wrote:
>
> Not entirely sure what you're asking for, but here's a simple routine
> that plots a Poincare section for a pair of ODEs with vector field (f,g):
>
> PoincareSection[{f_,g_}, {t_,t0_,tmax_,dt_}, {x_,x0_}, {y_,y0_}] :=
>    Module[{xsoln, ysoln},
>     {xsoln, ysoln} = {x, y} /. First@
>     NDSolve[{x'[t] == (f /. {x -> x[t], y -> y[t]}),
>              y'[t] ==(g /. {x -> x[t], y -> y[t]}),
>              x[0]==x0, y[0]==y0}, {x, y},
>              {t, t0, tmax}, MaxSteps -> Infinity];
>     ListPlot[Table[{xsoln[t], ysoln[t]}, {t, t0, tmax, dt}]]]
>
> And this is the classic example with Duffing's equation:
>
> PoincareSection[{y, x - x^3 - 0.2y + 0.3Cos[t]},{t,0,3000,2Pi},
>     {x, -1}, {y, 1}]
>
> ---
> Selwyn Hollis
>
> ckkm wrote:
> > Do you have some package that helps me vizualize subj. when i start from
> > motion equations or even Hamiltonian? Thanks.
> > __________________________________________________________________ ckkm
> > ICQ#: 54326471 Current ICQ status: +
> > __________________________________________________________________
> >
> >
> >
> >
> >
> >

```

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