We have done analysis in the past where we've computed an approximation for Gaussian curvature of a surface in Cartesian coordinates.
What we've been doing for Cartesian (in Matlab) is
[fu,fv] = gradient(Z)
[fuu, fuv] = gradient(fu)
[fvu,fvv] = gradient(fv)
GC = (fuu*fvv - fuv*fuv)/(1 + fu^2 + fv^2)
(more or less, trying to simplify the equations for AMF)
So now I have a surface that I'm modeling in cylindrical coordinates, and I can do the same thing as above for R as a function of Theta and Z. The problem is that it's only taking into account the change in R, not the fact that there is curvature inherent in it being a cylinder.
Looking on Wolfram
(equations 27, 32 and 37 and thereabouts), it seems like there's a centripetal component that I don't know how to apply. Dividing by the (constant?) radius doesn't seem like it would work, so I think I'm missing something.
Any help would be appreciated, either explaining how to modify these equations to work correctly, or some other approximation that has worked for you.