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MathGroup Archive 2001

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Parametric Plot Again

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27096] Parametric Plot Again
  • From: Winston Garira <uceswga at ucl.ac.uk>
  • Date: Sun, 4 Feb 2001 02:58:22 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

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





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