# A Restricted Four-body Problem for the Figure-eight Choreography

*2021, Volume 26, Number 3, pp. 222-235*

Author(s):

**Lara R., Bengochea A.**

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.

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