Polyhedral representation of invariant manifolds applied to orbit transfers in the Earth-Moon system

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. This work proposes and describes an intuitive polyhedral interpolative approach for each state component associated with manifold trajectories, both in two and in three dimensions. An adequate grid of data, coming from the numerical propagation of a finite number of manifold trajectories, is employed. Accuracy of this representation is evaluated with reference to the invariant manifolds associated with a two-dimensional Lyapunov orbit and a three-dimensional Halo orbit, and is proven to be satisfactory, with the exclusion of limited regions of the manifolds. As a first, preliminary application, the polyhedral interpolation technique allows identifying the orbits in the proximity of the interior collinear libration point as either asymptotic, transit, or bouncing trajectories. Then, two applications to orbital maneuvering are addressed. First, the globally optimal two-impulse transfer between a specified low Earth orbit and a Lyapunov orbit (through its stable manifold) is determined. Second, the minimum-time low-thrust transfer from the same terminal orbits is found using again the stable manifold. These applications prove the effectiveness of the polyhedral interpolative technique and represent the premise for its application also to different problems involving invariant manifold dynamics.