A Cylindrical Distribution for Uncertainty Representation at Equilibria of the Circular Restricted Three-Body Problem

Space situational awareness (SSA) relies on accurate and efficient uncertainty realism and propagation (UR&P). In the cislunar domain, there is growing interest in the use of orbits near the collinear libration points, which are relative equilibria in the simplified circular restricted three-body model. These equilibria are hyperbolic and therefore possess dynamical structures in phase space that separate the flow and present difficulties for UR&P. In this paper, we build on prior efforts to define a canonical distribution on a cylindrical space given by the application of normal form theory at a collinear equilibria. The canonical distribution is constructed to have components with disjoint support on the phase space, each of which properly represents the characteristic dynamics for the specific subset of phase space. This is achieved by a product of a multivariate folded normal distribution and conditional normal and von Mises distributions. Comparisons to a regularized distribution, the generalized Bernoulli-Gauss-von Mises, are made.