From Brake to Syzygy

Richard Moeckel (1) , Richard Montgomery (2) , Andrea Venturelli (3)

1 UMN-MATH - School of Mathematics
2 UC Santa Cruz - University of California [Santa Cruz]
3 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

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 Poincaré 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.

Mots clés: Celestial mechanics; three-body problem; brake orbits; syzygy

Domaines: Systèmes dynamiques [math.DS]

Richard Moeckel, Richard Montgomery, Andrea Venturelli. From Brake to Syzygy. Archive for Rational Mechanics and Analysis, 2012. ⟨hal-00619219⟩