  This work is the sequel of a previous investigation of stationary and
cylindrically symmetric vortex configurations for simple models representing an
incompressible non-relativistic superconductor in a rigidly rotating
background. In the present paper, we carry out our analysis with a generalized
Ginzburg-Landau description of the superconductor, which provides a
prescription for the radial profile of the normal density within the vortex.
Within this framework, it is shown that the Bogomol'nyi limit condition marking
the boundary between type I and type II behavior is unaffected by the rotation
of the background.
