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 calc ulation 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 subha rmonic solutions bifurcate from these elliptic modes at a dense set of parameter values near the equilibrium. Together with the linear stabi lity of the equilibrium, the ellipticity and subharmonic bifurcations of the isosceles synchronous normal modes justify theoretically the ro bustness of small clusters of sedimenting spheres that were observed e xperimentally as well as in computational studies. (C) 1995 Academic P ress, Inc.