Is it possible to express the mean curvature of a surface of revolution in terms of the first derivative of the polar tangential angle?


To be specific: Let $r=u(\theta)$ be a polar curve in the first quadrant of the xy-plane. The surface of revolution is generated by rotating this curve around the y axis. Let $\psi$ be the polar tangential angle, the angle between the tangent to the curve at a point and the ray from the origin to the point. Can the mean curvature be expressed as a first derivative of $\psi$?


Any suggestions or references appreciated.



mean curvature and polar tangential angle
Yes, it is true $H=F(u,\theta,\psi,\psi')$.


You ask for suggestion: *Calculate both principle curvatures,* 
$k\_1=k\_1(u,\theta,\psi)$ *and* $k\_2=k\_2(u,\theta,\psi,\psi')$.
Here $k\_2$ is the curvature of original curve $r=u(\theta)$
and $k\_1$ is principle curvature in the normal direction.


