Creating a Vector Field from a 3D Parametric Equation

[theobserver]

I am trying to turn a 3D parametric equation into a vector field for an experiment, but I am not having much luck. [x,y,z]=[r*cos(u),r*sin(u),a*u] is the equation, I'm using grapher on the Mac. I want it all going in a helix, which is what the equation is for.

Thanks!

 

[Rasalhague]

Not quite an answer to your question I'm afraid, but just in case it's any help, you can plot a vector field like this in Mathematica:

VectorPlot3D[{Norm[{x, y, z}]*Cos[ArcTan[x, y]], 
  Norm[{x, y, z}]*Cos[ArcTan[x, y]], ArcTan[x, y]}, {x, -9, 
  9}, {y, -9, 9}, {z, -9, 9}]

Wolfram Alpha didn't do anything when I tried it there just now, although it does plot the parametric equation with

ParametricPlot3D[{Cos[u],Sin[u],u}, {u, 0, 9}]

(taking r = a = 1).

 

[Unrest]

I am trying to turn a 3D parametric equation into a vector field for an experiment, but I am not having much luck. [x,y,z]=[r*cos(u),r*sin(u),a*u] is the equation, I'm using grapher on the Mac. I want it all going in a helix, which is what the

Hello again :)

Maybe it would help to explain the purpose a bit clearer. There's no unique way to convert a helix to a vector field. What do you want the vector field to look like? Should it fill all space or just exist on the curve? Should it be tangent to the curve at points on the curve?

If you simply want to plot the equation directly to get a picture of the helix then you don't need any extra math, the equation is already in an ideal form for parametric plotting. Just look up the manual for Grapher, equivalent to Rasel's ParametricPlot3D example.