  High-inclination circumplanetary orbits that are gravitationally perturbed by
the central star can undergo Kozai oscillations---large-amplitude, coupled
variations in the orbital eccentricity and inclination. We first study how this
effect is modified by incorporating perturbations from the planetary
oblateness. Tremaine et al. (2009) found that, for planets with obliquities >
68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to
eccentricity perturbations over a finite radial range, and execute
large-amplitude chaotic oscillations in eccentricity and inclination. In the
hope of making that treatment more easily understandable, we analyze the
problem using orbital elements, confirming this threshold obliquity.
Furthermore, we find that orbits inclined to the Laplace plane will be unstable
over a broader radial range, and that such orbits can go unstable for
obliquities less than 68.875 degrees. Finally, we analyze the added effects of
radiation pressure, which are important for dust grains and provide a natural
mechanism for particle semimajor axes to sweep via Poynting-Robertson drag
through any unstable range. We find that generally the effect persists;
however, the unstable radial range is shifted and small retrograde particles
can avoid the instability altogether. We argue that this is occurs because
radiation pressure modifies the equilibrium Laplace plane.
