  We present new analytical three-dimensional solutions of the
magnetohydrostatic equations, which are applicable to the co-rotating frame of
reference outside a rigidly rotating cylindrical body, and have potential
applications to planetary magnetospheres and stellar coronae. We consider the
case with centrifugal force only, and use a transformation method in which the
governing equation for the "pseudo-potential" (from which the magnetic field
can be calculated) becomes the Laplace partial differential equation. The new
solutions extend the set of previously found solutions to those of a
"fractional multipole" nature, and offer wider possibilities for modelling than
before. We consider some special cases, and present example solutions.
