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M. D. Melita, J.C.B. Papaloizou (U. London)
A general model of the dynamics of a narrow-eccentric ring is presented. We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global m=1 mode which can be seen as originating from a standing wave superposed on an axisymmetric background. Our model includes the external perturbations by neighbouring satellites and the dissipation due to inelastic inter-particle collisions. Two main conditions for the ring to be able to maintain a steady m=1 normal mode are obtained. One can be expressed as an integral condition for the normal mode pattern to precess uniformly, which requires the correct balance between the differential precession induced by the oblateness of the central planet, self-gravity and collisional effects. The other condition is for the steady maintainance of the non-zero radial action that the ring contains because of its finite eccentricity. This requires a balance between injection due to eccentric resonances arising from external satellites and additional collisional damping associated with the presence of the m=1 mode. We estimate that such a balance can occur in the epsilon-ring of Uranus, given its currently observed physical and orbital parameters.
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.