Revolve line around axis in sinusoidal fashion?

[member 428835]

Hi PF!

I have a vector valued function $f(s) = r(s)\hat r + z(s)\hat z$ that plots a line in the $r$,$z$ plane when I use ParametricPlot. I'd like to plot this line into a surface, so that it revolves around the $z$ axis, but in a sinusoidal fashion. Basically I'd like to revolve it around the $z$ axis as $\cos(l \theta) : l = 0,1,2...$. So $l=0$ would imply axisymmetric, while $l>0$ would imply a different sort of symmetry.

Thanks for your help!

 

[mmwave]

Hi there!

It sounds like you are trying to create a helical surface using your vector valued function. To do this, you can use the RevolutionPlot3D function in Mathematica. This function allows you to create a surface by revolving a curve around a specified axis.

In your case, you would want to specify the axis of rotation as the z-axis and use your function as the curve to be revolved. The syntax for RevolutionPlot3D would be something like this:

RevolutionPlot3D[{r(s), 0, z(s)}, {s, smin, smax}, {θ, 0, 2π}, RevolutionAxis -> {0, 0, 1}]

Here, smin and smax would be the limits of your parameter s, and θ would be the angle of rotation around the z-axis. You can also specify the number of rotations (l in your case) by changing the upper limit of θ.

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