Stability of Normal Modes and Subharmonic Bifurcations in the 3-Body Stokeslet Problem

The authors show that the isosceles synchronous periodic solutions of the 3-body Stokeslet problem are elliptic near the equilibrium. A calculation going beyond group-theoretic considerations is given to decide the stability of the isosceles synchronous and the instability of the isosceles asynchronous normal modes. Moreover, it is shown that subharmonic solutions bifurcate from these elliptic modes at a dense set of parameter values near the equilibrium. Together with the linear stability of the equilibrium, the ellipticity and subharmonic bifurcations of the isosceles synchronous normal modes justify theoretically the robustness of small clusters of sedimenting spheres that were observed experimentally as well as in computational studies.