       Re: Poincare sections

• To: mathgroup at smc.vnet.net
• Subject: [mg37305] Re: [mg37276] Poincare sections
• From: Selwyn Hollis <selwynh at earthlink.net>
• Date: Tue, 22 Oct 2002 04:47:59 -0400 (EDT)
• References: <200210210630.CAA12321@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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==x0, y==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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