All I can add...
Is the qualitative observation that when an object in orbit fragments, like a comet losing its volatiles and releasing a cloud of meteoritic gravel,
they tend to disperse themselves along the orbit as a spindle-shaped cloud of particles that eventually evolves into a flat ring around the orbited body. Saturn's rings are probably the resulting debris of prior satellite collisions in the ring plane, along with material that never managed to accrete into compact bodies. Apparently, this process is still going on. Keep us informed on the results of your calculations.