From Brake to Syzygy
  In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincar\'e map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits. 
Richard Moeckel (UMN-MATH), Richard Montgomery (UCSC), Andrea   Venturelli (LANLG)
math.DS