Orbital parameter characterization and objects cataloging for Earth-Moon collinear libration points

Owing to the chaotic and non-integrable nature of three-body dynamics, the conventional Keplerian elements are rendered inadequate for cataloging cislunar space objects. Currently, there has been a conspicuous absence of universally recognized parameters for the characterization and cataloging of such objects, thereby posing an urgent challenge to cislunar space situational awareness. This paper proposes a novel approach to parameterize the orbits of Earth-Moon collinear libration points by leveraging the theoretical frameworks of canonical transformations. First, under the Hamiltonian-form dynamical equations of the libration point, symplectic transformations are employed to extract 3 modes of motion from locally linearized part. A subsequent canonical transformation then decouples the hyperbolic invariant manifold from the center manifold within the nonlinear remainder. Finally, 6 characteristic parameters obtained via action-angle variables are established in a bijective correspondence with the state variables, where two parameters characterize the motion of the invariant manifold and four parameters characterize the motion of the central manifold. Furthermore, a distribution map of the Earth-Moon libration point orbits is drawn utilizing Poincaré sections, which can be used to describe the distribution of libration point object. Simulation results demonstrate that the proposed parameters are not only applicable to orbit identification and object cataloging but also exhibit remarkable consistency and robustness against variations in observation arc length and observational errors.