  We classify all rotational surfaces in Euclidean space whose principal
curvatures $\kappa_1$ and $\kappa_2$ satisfy the linear relation
$\kappa_1=a\kappa_2+b$, where $a$ and $b$ are two constants. We give a
variational characterization of these surfaces in terms of its generating
curve. As a consequence of our classification, we find closed (embedded and not
embedded) surfaces and periodic (embedded and not embedded) surfaces with a
geometric behaviour similar to Delaunay surfaces.
