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>