Re: Parametric Plot Again
- To: mathgroup at smc.vnet.net
- Subject: [mg27138] Re: Parametric Plot Again
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Wed, 7 Feb 2001 02:12:44 -0500 (EST)
- References: <4Xnf6.3581$l32.32692@ralph.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Winston,
I should have been more explicit.
What you need is
xd[t_] = x1[t] /. pend[[1]];
xdd[t_]= x1'[t] /. pend[[1]];
xr[t_] = x2[t] /. pend[[1]];
xrd[t_]= x2'[t] /. pend[[1]];
You see,
pend is
{{ x1 -> InterpolatingFunction[{{0., 5000.}}, "<>"],
x2 -> InterpolatingFunction[{{0., 5000.}}, "<>"] }}
and
pend[[1]] is
{ x1 -> InterpolatingFunction[{{0., 5000.}}, "<>"],
x2 -> InterpolatingFunction[{{0., 5000.}}, "<>"] }
Regards,
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Winston Garira" <uceswga at ucl.ac.uk> wrote in message
news:4Xnf6.3581$l32.32692 at ralph.vnet.net...
> Hi Allan,
>
> Thank for replying to my request. I have tried to make the change that you
> recommended by making the following changes:
>
> xd[t_] = x1[t] /. pend[[1]];
> xdd[t_]= x1'[t] /. pend[[2]];
> xr[t_] = x2[t] /. pend[[3]];
> xrd[t_]= x2'[t] /. pend[[4]];
>
> But still the ParametricPlot[{xd[t], xdd[t]}, {t,0,100}];
>
> does not work. Could it be that I misunderstood the change that you
> recommended?
>
> Winston
>
>
> > > I am trying to solve a system of two coupled pendulums using the
NDSolve.
> > > command. If I replace the Plot[{xd[t],xr[t]},{t,0,100}] with
> > > ParametricPlot[{xd[t],xr[t]},{t,0,100}] it does not work. Can someone
tell
> > > me why the ParametricPlot command does not work in this case. I need
to
> > > make parametric plots for this system.
> > >
> > > Thanking you in annticipation
> > >
> > > Winston
> > >
> > >
> > > Pends[init1_, init2_, time_, k_, {c_, w_, p_}]:=
> > > Module[{},
> > > pend=NDSolve[{x1''[t]+ c x1'[t]+ p Sin[x1[t]]==k(x2[t]-x1[t]),
> > > x2''[t]+ c x2'[t]+ p Sin[x2[t]]==k(x1[t]-x2[t]),
> > > x1[0]==init1[[1]], x1'[0]==init1[[2]],
> > > x2[0]==init2[[1]], x2'[0]==init2[[2]]},
> > > {x1, x2},
> > > {t,0,time}, MaxSteps->200000];
> > > xd[t_] := Evaluate[x1[t] /. pend];
> > > xdd[t_]:= Evaluate[x1'[t] /. pend];
> > > xr[t_] := Evaluate[x2[t] /. pend];
> > > xrd[t_]:= Evaluate[x2'[t] /. pend];
> > > ];
> > >
> > >
> > > c=0.1; w=0.5; p=1.9;
> > >
> > > Pends[{1.57,0}, {-1.57,0}, 5000,0.6, {c,w,p}];
> > > Plot[{xd[t],xr[t]},{t,0,100},
> > > PlotStyle\[Rule]{RGBColor[1,0,0.3],RGBColor[0,0.5,1]}];
> > >
> > >
> > >
> > > W.GARIRA
> > > E-mail: w.garira at ucl.ac.uk
> > > phone : +44-(0)20-7679-2521
> > > ___________________________________________________
> > >
> > >
> > >
> > >
>
>
> >
> > Winston,
> > You are getting listed values like
> >
> > xd[4]
> >
> > {1.24463}
> >
> > Plot lets us get away with this (it flattens the input), but
ParametricPlot
> > assumes that {{x1[t]},{x2[t]}} is an error for something like
> > {{x1[t]`y1[t]},{x2[t], y2[t]}} .
> >
> > One way out is to replace
> >
> > xd[t_] := Evaluate[x1[t] /. pend];
> > etc
> >
> > with
> >
> > xd[t_] = x1[t] /. pend[[1]];
> >
> > etc
> >
> > (the Evaluate is unnecessary if we use = instead of :=)
> >
> > --
> > Allan
> > ---------------------
> > Allan Hayes
> > Mathematica Training and Consulting
> > Leicester UK
> > www.haystack.demon.co.uk
> > hay at haystack.demon.co.uk
> > Voice: +44 (0)116 271 4198
> > Fax: +44 (0)870 164 0565
>
>
>
>
>