I'm having trouble conceptualizing the variables involved with this system, and I was wondering if some expertise might make the problem much simpler than I believe it to be. Two massive spherical bodies (Osmium, minimum radius 900km, 5.08m/s^2 surface gravity) orbit each other with a solid or semi-solid washer-shaped ring of negligible mass between them, spinning rapidly. The ring is slightly tilted in the direction of the spheres' orbits. I think gravity exerts torque on the spinning ring which is shifted by its gyroscopic nature to an axis perpendicular to both orbit and rotation, but there is where I get lost because I can't picture what that will do. (I know it depends on the direction of the rotation) I've been looking at things like apsidal precession, or trying to figure out the shape of a theoretical asteroid belt before I weld all the bits together, but I just can't picture the motion. If this model doesn't immediately deteriorate in all cases, what are the constraints of stability? Does the ring have to be entirely outside the binary orbit? If it's all about trial and error, how do I go about experimenting with this or any other model? Thank you for your interest in this question, I hope it isn't just "another ridiculous three-body problem."