On the existence of generalised syzygies in the planar three-body problem - Tsygvintsev, Alexei (Comptes Rendus. Mathématique)
We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm–Liouville theory.