Stability of normal modes and subharmonic bifurcations in the 3-body Stokeslet problem (Q1900178)

The authors investigate a model related to the sedimentation under gravity of spheres in a highly viscous fluid. Motivated by experimental and analytic investigations they study the motions of 3 identical point particles. Due to the symmetry of the model it is possibly to reduce the originally 6-dimensional system of ODEs with one conserved quantity to a 2-dimensional fixed point space of synchronous or asynchronous solutions, where phase plane analysis can be applied. By calculating the small oscillations close to the synchronous and asynchronous periodic orbits it is shown that the synchronous solutions are elliptic and infinitely many branches of subharmonic solutions bifurcate from these normal modes.