Analytical Potential-Density Pairs for Flat Rings and Toroidal
  Structures
  The Kuzmin-Toomre family of discs is used to construct potential-density
pairs that represent flat ring structures in terms of elementary functions.
Systems composed of two concentric flat rings, a central disc surrounded by one
ring and a ring with a centre of attraction are also presented. The circular
velocity of test particles and the epicyclic frequency of small oscillations
about circular orbits are calculated for these structures. A few examples of
three-dimensional potential-density pairs of "inflated" flat rings (toroidal
mass distributions) are presented.
