# Manipulate Parametric Plot of Complex Function

I have a complex function that I would like to understand better using Mathematica's graphing capabilities, but I'm not having any luck with using "animate".

The function I am studying is defined as

hdot[ω_, t_] :=
hdot[ω, t] =
I ω Cos[t ω] - ω Sin[t ω]


I was able to figure out how to use "Manipulate" to view the function at different times, but now I would like to animate this. Here is what I have for Manipulate:

Manipulate[
ParametricPlot[{Re[hdot[ω, t]],
Im[hdot[ω, t]]}, {ω, -4, 4}, AspectRatio -> 1], {t,
0, 10, 0.25}]


I had tried to follow the examples available in Mathematica's documentation on "Manipulate" to animate my graphic, such as using a controller:

Manipulate[
ParametricPlot[{Re[hdot[ω, t]],
Im[hdot[ω, t]]}, {ω, -4, 4}, AspectRatio -> 1], {t,
0, 10, 0.25}, ControllerMethod -> "Cyclic"]


but this doesn't run automatically (it is, in fact, no different than my first attempt at using "Manipulate"). I am sure I am missing a link between using "Manipulate" and "ParametricPlot" for representing complex functions, but I can't see it yet, and I would appreciate any help.

• I you click on the small cross of the cursor, you can have the run symbol which will animate your graph. If this is what you intend to do be more explicit – cyrille.piatecki Sep 20 '16 at 18:30
• Oh thank you, that was what I was looking for - something to play automatically. I didn't know the cross expanded options, thanks. – Kaszt Sep 20 '16 at 20:10