  Many small moonlets, creating propeller structures, have been found in
Saturn's rings by the Cassini spacecraft. We study the dynamical evolution of
such 20-50m sized bodies which are embedded in Saturn's rings. We estimate the
importance of various interaction processes with the ring particles on the
moonlet's eccentricity and semi-major axis analytically. For low ring surface
densities, the main effects on the evolution of the eccentricity and the
semi-major axis are found to be due to collisions and the gravitational
interaction with particles in the vicinity of the moonlet. For large surface
densities, the gravitational interaction with self-gravitating wakes becomes
important.
  We also perform realistic three dimensional, collisional N-body simulations
with up to a quarter of a million particles. A new set of pseudo shear periodic
boundary conditions is used which reduces the computational costs by an order
of magnitude compared to previous studies. Our analytic estimates are confirmed
to within a factor of two.
  On short timescales the evolution is always dominated by stochastic effects
caused by collisions and gravitational interaction with self-gravitating ring
particles. These result in a random walk of the moonlet's semi-major axis. The
eccentricity of the moonlet quickly reaches an equilibrium value due to
collisional damping. The average change in semi-major axis of the moonlet after
100 orbital periods is 10-100m. This translates to an offset in the azimuthal
direction of several hundred kilometres. We expect that such a shift is easily
observable.
