Relative Transfer Singularities and Multi-Revolution Lambert Uniqueness

Solving boundary value transfer problems is fundamental to the study of inertial and relative motion of satellites. It is well-known that singularities exist within the linearized relative motion equations for determining transfers. After reviewing these singularities and their implications for reachability and propagation of uncertainty, we present the relationship between singularities, infinite non-uniqueness within the linearized relative motion model, and uniqueness of corresponding multiple revolution Lambert solutions in the two-body dynamics. We extend this result to a further class of second order differential equations and associated boundary value problems. We conclude by demonstrating the appearance of these transfer singularities in a specific relative orbit reconfiguration problem, and give heuristics for delta-v optimal choices of transfer duration and initiation time in consideration of singularities.