Construction of Periodic Orbits, Problems of Stability and Period Determination, in the Elliptical Non-Planar Restricted Problem

Abstract

AbstractPeriodic orbits in a fixed frame are constructed in the vicinity of nonperiodic solutions of the non perturbed problem. In a first phase, approximate initial conditions are found and in a second phase more accurate initial conditions obtained are used in order to check the periodic orbit by numerical integration of the three-body problem. Some peculiar solutions are found, for example, orbit with nearly zero angular momentum. A study of stability of periodic solutions is proposed with an approximation of the monodromy matrix Φ (T,o),not requiring numerical integration of the 6x6 variational linear system. Finally, some numerical problems of period determination are outlined.