Linear stability of ring systems with generalized central forces

We analyze the linear stability of a system of n equal mass points uniformly distributed on a circle and moving about a single massive body placed at its center. We assume that the central body makes a generalized force on the points on the ring; in particular, we assume the force is generated by a Manev's type potential. This model represents several cases, for instance, when the central body is a spheroid or a radiating source. The problem contains 3 parameters, namely, the number n of bodies of the ring, the mass factor mu, and the radiation or oblateness coefficient epsilon. For the classical case (Newtonian forces), it has been known since the seminal work of Maxwell that the problem is unstable for n = 6. For n = 7 the problem is stable when mu is within a certain interval. In this work, we determine the region (epsilon, mu) in which the problem is stable for several values of n. Unstable cases (n <= 6) may become stable for negative values of epsilon.