Re: Re: Poincare sections
- To: mathgroup at smc.vnet.net
- Subject: [mg37361] Re: [mg37335] Re: Poincare sections
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Fri, 25 Oct 2002 02:46:54 -0400 (EDT)
- References: <200210210630.CAA12321@smc.vnet.net> <ap5asb$3un$1@smc.vnet.net> <200210240655.CAA05047@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
My deepest apologies, Jens. You're right---the function I gave only
plots Poincare *time* sections. However, it *does work* for autonomous
(2x2) systems; it just doesn't do anything interesting.
Regards
Selwyn
Jens-Peer Kuska wrote:
> 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: +
>>>__________________________________________________________________
>>>
>>>
>>>
>>>
>>>
>>>
>>
>
>
- References:
- Poincare sections
- From: "ckkm" <ckkm@post.cz>
- Re: Poincare sections
- From: Jens-Peer Kuska <kuska@informatik.uni-leipzig.de>
- Poincare sections