Polyhedral representation of invariant manifolds for Earth-moon mission analysis

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth-Moon system and in alter-native multibody environments. Several researches have been focused on this topic in the last decades, and some space missions have already taken ad-vantage of the results of these studies. Recent efforts have been devoted to de-veloping a suitable representation for the manifolds, which would be extremely useful for mission analysis and optimization. This work proposes and describes an intuitive polyhedral interpolative approach for each state component asso-ciated with manifold trajectories, both in two and in three dimensions. An ade-quate grid of data, coming from the numerical propagation of a finite number of manifold trajectories, is employed. With regard to the planar manifold asso-ciated with the Lyapunov orbit at the interior collinear libration point , accu-racy of this representation is evaluated, and is proven to be satisfactory, with the exclusion of limited regions of the manifold. The polyhedral interpolation technique has several applications, outlined in this work, and three of them are illustrated in this paper. First, transit orbits in the phase space are identified at different locations in the synodic reference system. Second, the globally optimal two-impulse transfer between a specified low Earth orbit and a Lyapunov orbit of given energy is determined. Third, six homoclinic trajectories connected with the previously mentioned Lyapunov orbit are detected in a straightforward way. These three applications prove the effectiveness of the polyhedral interpolative technique and represent the premise for its application also to more challenging problems