RAPID and informed trajectory design strategies within multi-body systems often benefit from the use of Poincaré maps.

Specifically, Poincaré mapping enables visualization of a large set of trajectories, generated in a given dynamical system, via their intersections with a hyperplane [1]. When constructed appropriately, Poincaré maps simplify the representation and analysis of fundamental motions in a chaotic dynamical system. For instance, consider a two-dimensional map that uniquely represents a state along a planar trajectory at a single value of a constant of motion in an autonomous system. Patterns that emerge on this map may reveal the characteristics of the solution space and the existence of fundamental dynamical structures [2–6]. Furthermore, a trajectory designer is often interested in assessing the fundamental geometries exhibited by solutions captured on the map along with their regions of existence. Such insight supports selecting individual arcs to construct an initial guess for an end-to-end trajectory [3, 7–10].