# Stationary Motion of a Self-gravitating Toroidal Incompressible Liquid Layer

*2012, Volume 17, Number 5, pp. 397-416*

Author(s):

**Fusco G., Negrini P., Oliva W. M.**

We consider an incompressible fluid contained in a toroidal stratum which is only subjected 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 approximately a round torus (with radii $r$, $R$ and $R \gg r$) 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 $R$ that connects the centers of the cross sections of the torus.
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