Plot a vector valued function in cylindrical coordinates

[member 428835]

Hi PF!

I have a function $f(s,\theta) = r(s,\theta)\hat r + t(s,\theta)\hat \theta + z(s,\theta)\hat z$. How can I plot such a thing in Mathematica? Surely there's an easier way than decomposing $\hat r, \hat \theta$ into their $\hat x,\hat y$ components and then using ParametricPlot3D?

 

[mmwave]

Hi there,

Thank you for your question! There is indeed an easier way to plot a function of the form $f(s,\theta) = r(s,\theta)\hat r + t(s,\theta)\hat \theta + z(s,\theta)\hat z$ in Mathematica. You can use the built-in function VectorPlot3D, which allows you to plot vector fields in three dimensions.

To use this function, you will need to define your function as a vector field, with the components r, t, and z as the x, y, and z components respectively. For example, you could define your function as follows:

f[s_, \[Theta]_] := {r[s, \[Theta]], t[s, \[Theta]], z[s, \[Theta]]}

Then, you can use VectorPlot3D to plot the vector field as follows:

VectorPlot3D[f[s, \[Theta]], {s, smin, smax}, {\[Theta], \[Theta]min, \[Theta]max}]

Where smin, smax, \[Theta]min, and \[Theta]max are the minimum and maximum values for s and \[Theta] that you want to plot.

I hope this helps! Let me know if you have any further questions.