Hydrodynamic interactions and some new periodic structures in three particle sediments

It is well known that the motion of three particles sedimenting in a Stokes fluid is of a simple periodic function of time if the initial configuration is a horizontal, equilateral triangle. We use the method of induced forces to show that if this ititial configuration is made less symmetric then many much more complex structures, which are still periodic in time, may result which involve a sequence of inequivalent configurations. This confirms that the horizontal isosceles triangle configuration is remarkably robust against perturbations.