Animate a Vectorfield with VectorPlot3d , Scaling the Vectors

Questions
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1

Hey there,

i want to animate the Variation of a Vectorfield by controlling the Parameter m.

So far this is what i got and it works

 f[x_, y_, z_, g_, m_,v_] := 
   {((x)^2 - m), x*y,x*z}*(g*v^2)/
     (2*(g^2*((x)^2 - m)^2 + (v*y)^2 + (v*z)^2)^(3/2));   
plots = 
  Table[
    Show[
      VectorPlot3D[
        f[x, y, z, 1, e, 1], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
        VectorColorFunction -> Hue]], 
    {e, -5, 5, 1}];
ListAnimate[plots];
Export["Test.gif", plots, ImageResolution -> 200]

The problem is the scaling of the Vectors. Mathematica scales them in each frame. You cannot compare 2 picture directly because the size is at a different scaling.

I want the size of the vectors, in every frame, relative to e.g. the biggest possible vector in the whole animation.
I used VectorScale-> but could not get it right.

Thank you for your Help and kind regards,
max

2

If you have a problem with scaling you must add “Plot range”.

f[x_, y_, z_, g_, m_, v_] :=
 {((x)^2 - m), x*y, x*z}*(g*v^2)/(2*(g^2*((x)^2 - m)^2 + (v*y)^2 + (v*z)^2)^(3/2));

 Animate[VectorPlot3D[f[x, y, z, 1, m, 1], {x, -5, 5}, {y, -5, 5}, {z, -5, 5},VectorColorFunction -> Hue, PlotRange -> 5], {m, -5, 5, 1},AnimationRunning -> False]

Export to Animation.

ANIM = Table[
   VectorPlot3D[
    f[x, y, z, 1, m, 1], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
    VectorColorFunction -> Hue, PlotRange -> 5], {m, -5, 5, 0.25}];
Export["Test.gif", ANIM, ImageResolution -> 200]
3

This does not solve the Problem. The Problem is the different size of the vectors in each Frame.

But thank you for replying and trying to solve my problem !
Best regards,
max

4

In Documentation Center is written:

With the vector scaling function set to None, then all vectors have the same size.

Animate[VectorPlot3D[
 f[x, y, z, 1, m, 1], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
 VectorColorFunction -> Hue, PlotRange -> 5, 
 VectorScale -> {Small, Automatic, None}], {m, -5, 5, 0.5}, 
AnimationRunning -> False]

or

Animate[VectorPlot3D[
  f[x, y, z, 1, m, 1], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, 
  VectorColorFunction -> Hue, PlotRange -> 5, 
  VectorScale -> {Small, Small, None}], {m, -5, 5, 0.5}, 
 AnimationRunning -> False]

I hope it will help.