Defining Admissible Control Regions Using Hamiltonian Normal Forms of the Circular Restricted Three-Body Problem

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Abstract This work introduces the use of normal-form coordinates in the circular restricted three-body problem as local dynamical features for trajectory characterization. In particular, the saddle coordinates of the normal form are leveraged to define admissible-control regions, i.e., subsets of impulsive maneuvers bounded in both magnitude and time, such that trajectories within each subset exhibit dynamically similar behavior. The proposed methodology results in a two-point boundary value problem formulated in mixed Cartesian and normal-form coordinates. To enable rapid maneuver generation, polynomial approximations are constructed for the resulting $$\Delta \textbf{v}$$ Δ v solution surfaces. Additional polynomial approximations are introduced to enforce maneuver-magnitude constraints efficiently within the admissible-control framework. The accuracy and robustness of all approximations are examined extensively across multiple maneuver windows and libration-point regions. The resulting framework provides a computationally efficient approach for generating and characterizing cislunar maneuvers with embedded qualitative dynamical information, without reliance on extensive Monte Carlo simulations or sample-rejection strategies.

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