On the stationary motion of a self-gravitating toroidal stratum

Abstract

We consider an incompressible fluid contained in a toroidal stratum and subject only to Newtonian self-attraction. Under the assumption of infinitesimal thickness of the stratum we show the existence of stationary motions during which the stratum is approximatly a round torus (with radii

r, R and R >> r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R.