Orbital changes during hypersonic aerocruise

A novel mathematical approach that allows the analysis of orbital changes occurring during an aerocruise maneuver to be conducted in two distinct stages is presented. In the first stage, the aerodynamic turn is determined using a nondimensional form of the equations of motion that is free of singularities, and the way in which speed, altitude, angle of attack, and thrust direction should be chosen to maximize the aerodynamic turn for a given propellant expenditure is demonstrated. In the second analysis stage, the aerodynamic turn is translated into changes in the orbital elements with respect to the equatorial plane; analytic solutions for the initial arguments of latitude that maximize the change in inclination and in the longitude of the ascending node are given. As the initial inclination decreases toward zero, the optimal location moves from the apex toward the node.