Re: Parametric List Plot??
- To: mathgroup at smc.vnet.net
- Subject: [mg126498] Re: Parametric List Plot??
- From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
- Date: Tue, 15 May 2012 04:53:15 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.boulbitch at iee.lu