Hamilton, D.P and A.V. Krivov 1996. Circumplanetary dust dynamics: Effects of solar gravity, radiation pressure, planetary oblateness, and electromagnetism. Icarus 123, 503-523.

We consider the motions of circumplanetary objects perturbed simultaneously by solar gravity, radiation pressure, planetary oblateness, and electromagnetic forces. Confining ourselves to the planar case, but retaining all nonlinear terms in the eccentricity, we rewrite the orbit-averaged equations for the sum of the four perturbations as a semicanonical system. We derive a conserved integral of the motion which is valid for initially elliptic orbits of arbitrary size and shape. This integral is used to investigate the phase space qualitatively, and to show how the eccentricity and apses line evolve for various strengths of the perturbation forces. We find several different classes of motion, and show that near certain critical initial conditions, small variations in parameters such as particle size or initial semimajor axis can cause dramatic changes in a particle's orbit. This effect is important in Saturn's E ring and for Phobos dust. We apply our model to dusty ejecta launched from several moons -- Phobos, Deimos, Elara, and Enceladus -- and to the motions of Elara itself. In each case, we compare our analytic results to numerical integrations of the full Newtonian equations of motion.
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