Periodic oscillations of particles settling under gravity in a viscous fluid

New periodic solutions of three spherical particles settling under gravity in a viscous fluid are found and their relation to chaotic dynamics of a cluster of three randomly distributed particles is shown. An analogue of this solution has not been detected in the point-particle approximation. However, the existence of such an unstable periodic orbit was previously suggested by Janosi et al., Phys.Rev. E,\textbf{56}, 2858 (1997) and was claimed to be responsible for the numerically observed chaotic scattering of three point-particles settling under gravity. The significance of periodic orbits for dynamics of sedimenting particles in other non-regular configurations is also illustrated by other examples.