Variation of parameters using complex exponentials to solve the perturbed two-body problem
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A new formulation of the variation of parameters method for the perturbed, Keplerian two-body problem is presented. Here, this unique formulation is based on a Complex Exponential solution previously derived by the authors 1. The Complex Exponential formulation provides an exact analytical solution to the unperturbed, Keplerian two-body problem and eliminates the singularities associated with the elliptic and hyperbolic trajectories that arise at zero eccentricity and zero inclination. We present the variation of parameters formulation and highlight the benefits of this approach compared with the classical developments.