Mathematica: plot and evaluate function of 2 variables

[hasidim]

Hi all,

I am trying to evaluate and plot a function of two variable in mathematica.

Function:

R(t,\theta) = a(t) + b(t)*Y_n(\theta)

Where a(t) and b(t) are functions (that I have evaluated already), and Y is the spherical harmonic for a given n, and R is the radius.

In mathematica I am unsure how to evaluate and plot a function of two variables in spherical coordinates. I attempted to use "SphericalPlot3D" to plot R as a function of \theta and \phi, and "Manipulate" to add a slider to adjust the time but am having no luck.

Any help would be APPRECIATED!

 

[Bill Simpson]

Is this something like what you are trying to do?

a[t_] := 2t; b[t_] := t^2; m = 1;(* < --- Substitute your functions here *)
R[t_, n_, m_, theta_, phi_] := a[t] + b[t]*SphericalHarmonicY[n, m, theta, phi]
Manipulate[SphericalPlot3D[R[t, n, m, theta, phi], {theta, 0, 2Pi}, {phi, 0, Pi}], {t, 0, 1}, {n, 0, 4, 1}]

Can you perhaps adapt this for what you need?

 

[hasidim]

Is this something like what you are trying to do?

a[t_] := 2t; b[t_] := t^2; m = 1;(* < --- Substitute your functions here *)
R[t_, n_, m_, theta_, phi_] := a[t] + b[t]*SphericalHarmonicY[n, m, theta, phi]
Manipulate[SphericalPlot3D[R[t, n, m, theta, phi], {theta, 0, 2Pi}, {phi, 0, Pi}], {t, 0, 1}, {n, 0, 4, 1}]

Can you perhaps adapt this for what you need?

That is pretty similar to what I have tried... but, I'll try copying that and modifying it.

As usual, I suspect that I am missing just one small detail.

 

[Bill Simpson]

If your modification doesn't work then divide the problem into simpler tasks.
Confirm that
SphericalPlot3D[SphericalHarmonicY[1, 2, theta, phi]], {theta, 0, 2Pi}, {phi, 0, Pi}]
plot matches http://mathworld.wolfram.com/SphericalHarmonic.html
and substitute a few other values for the 1 and 2.
Then try a simpler Manipulate example using a Real and Integer value from the Help and confirm that works. That might uncover some of your missing details.