  We examine the dynamics of a particle in a general rotating quadratic
potential, not necessarily stable or isotropic, using a general complex mode
formalism. The problem is equivalent to that of a charged particle in a
quadratic potential in the presence of a uniform magnetic field. It is shown
that the unstable system exhibits a rich structure, with complex normal modes
as well as non-standard modes of evolution characterized by equations of motion
which cannot be decoupled (non-separable cases). It is also shown that in some
unstable cases the dynamics can be stabilized by increasing the magnetic field
or tuning the rotational frequency, giving rise to dynamical stability or
instability windows. The evolution in general non-diagonalizable cases is as
well discussed.
