A state transition matrix using complex exponentials for the two-body problem
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Previously, a complex exponential solution was derived which unified the elliptic and hyperbolic trajectories into a single set of equations1 and provided an exact analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this Complex Exponential solution formulation, the State Transition Matrix has been derived and is presented. We present the analytical state transition matrix formulation and highlight the benefits of this approach compared with the classical developments.
author list (cited authors)
Henderson, T. A., Radice, G., & Junkins, J. L.