  We investigate regular configurations of a small number of particles settling
under gravity in a viscous fluid. The particles do not touch each other and can
move relative to each other. The dynamics is analyzed in the point-particle
approximation. A family of regular configurations is found with periodic
oscillations of all the settling particles. The oscillations are shown to be
robust under some out-of-phase rearrangements of the particles. In the presence
of an additional particle above such a regular configuration, the particle
periodic trajectories are horizontally repelled from the symmetry axis, and
flattened vertically. The results are used to propose a mechanism how a
spherical cloud, made of a large number of particles distributed at random,
evolves and destabilizes.
