Abstract:
In this work we introduce a planar restricted four-body problem where a massless
particle moves under the gravitational influence due to three bodies following the figure-eight
choreography, and explore some symmetric periodic orbits of this system which turns out to
be nonautonomous. We use reversing symmetries to study both theoretically and numerically a
certain type of symmetric periodic orbits of this system. The symmetric periodic orbits (initial
conditions) were computed by solving some boundary-value problems.
References