
Re: Parametric List Plot??
Posted:
May 15, 2012 4:54 AM


Hi, For some phase portraits I want to plot two lists of data in one plot (x and y axis). I found ParametricPlot for functions but need that parametric part combined with ListPlot..? Thanks in advance!
Hi, To the best of my knowledge, there is no such a function. There is, however, a simple work around. Say, for example, you need to solve this:
sol = NDSolve[{y''[t] == Sin[y[t]], y[0] == 1, y'[0] == 0}, y[t], {t, 0, 3 \[Pi]}][[1]]
{y[t] > \!\(\* TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.`", ",", "9.42477796076938`"}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable>False]\)[t]}
The result is the interpolation function. Now you need a numeric calculus package:
Needs["NumericalCalculus`"]
With this you easily find the numeric derivative, ND[ ], of the solution. Let us package it into a list With the following structure {...{y[t],y'[t]}...}:
lst = Table[{y[t] /. sol /. t > t1, ND[(y[t] /. sol), t, t1]}, {t1, 0, 2. \[Pi], 0.05}];
Here is your phase portrait:
ListPlot[lst]
Evaluate it.
Have fun, Alexei
Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L5326 Contern, LUXEMBOURG
Office phone : +35224542566 Office fax: +35224543566 mobile phone: +49 151 52 40 66 44
email: alexei.boulbitch@iee.lu

