Periodic orbits of particles settling under gravity in a viscous fluid

To understand basic features of the dynamics of particle systems settling under gravity in a very viscous fluid, it is useful to study simple models. A class of periodic orbits of three rigid spheres in a vertical plane is found numerically for certain intial configurations. The multipole expansion corrected for lubrication based on the Stokes equations is used. Basic features of the periodic solutions, including their sensitivity to small perturbations, are analyzed. It is shown that the same type of the periodic motion was observed elsewhere for a more complex system.