New families of periodic orbits in the 4-body problem emanating from a kite configuration

Abstract

By using analytical and numerical tools we show the existence of families of quasiperiodic orbits (also called relative periodic orbits) emanating from a kite configuration in the planar four–body problem with three equal masses. Relative equilibria are periodic solutions where all particles are rotating uniformely around the center of mass in the inertial frame, that is the system behaves as a rigid body problem, in rotating coordinates in general these solutions are quasiperidioc. We introduce a new coordinate system which measures (in the planar four–body problem) how far is an arbitrary configuration from a kite configuration. Using these coordinates, and the Lyapunov center theorem, we get families of quasiperiodic orbits, an by using symmetry arguments, we obtain periodic ones, all of them emanating from a kite configuration.