  This paper is concerned with difficulties encountered by engineers when they
attempt to predict the orientation of fibers in the creation of injection
molded plastic parts. It is known that Jeffery's equation, which was designed
to model a single fiber in an infinite fluid, breaks down very badly when
applied, with no modifications, to this situation. In a previous paper, the
author described how interactions between the fiber orientation and the
viscosity of the suspension might cause instability, which could result in the
simple predictions from Jeffery's equation being badly wrong. In this paper, we
give some rigorous proofs of instability using Floquet Theory. We also give an
example where the spectal radius of the monodromy operator is one, but there is
still non-linear instability.
