TABLE OF CONTENTS This section presents examples of precision-integrated, optimized low earth orbit (LEO) to geostationary earth orbit (GEO) minimum-time transfer and compares them to the solutions obtained by way of the averaging technique. A 10 ?2 g acceleration applied in a constant and continuous manner is taken as an example in order to generate fast subday transfers that could be flown with nuclear thermal propulsion upper stages. The six-state formulation used here allows the user to generate optimal transfers that first start from a given fixed location on the initial orbit while optimizing the arrival point on the target or final orbit. The analysis is further extended to optimize both departure and arrival points in order to obtain the overall minimum-time free-free solution. This requires the vanishing of the Lagrange multiplier adjoint to the mean longitude at both initial and final times with fixed initial time and optimized final time. These fast, few-revolution, five-state transfers are sensitive to initial and final orbital position, thereby necessitating the use of the full six-state dynamics. These exact results are then compared to the approximate solutions obtained using averaged dynamics with robust and fast convergence characteristics. These examples determine that the V s or transfer time solutions compare rather well, even for these short-duration transfers, but that the element time histories, and especially the eccentricity, are poorly simulated by the approximate solutions. Furthermore, due to the nature of the averaging technique, the sensitivity of the solution to...
