| It is well known that the use of aerodynamic forces to assist in orbital transfer can significantly reduce the fuel consumption as compared to a purely propulsive transfer. In the previously published literature, the analyses were done for either simplified cases or were numerically oriented and confined to the performance of a particular vehicle. Furthermore, the coupling effect between the space maneuver and the atmospheric maneuver has not been thoroughly analyzed, so that the results are often not globally optimal. In this study, the sole physical performance parameter that must be specified is the maximum lift-to-drag ratio of the vehicle. The generality of the results enables orbital flight and high atmospheric flight at hypersonic speeds to be considered as an integral problem in astrodynamics under a global optimization to find the combined optimal trajectory for the orbital transfer vehicle.; The use of Chapman's variables permits the formulation of a set of dimensionless equations for atmospheric flight with a smooth transition to flight in the vacuum. A spherical planet with a stationary, exponential atmosphere is assumed, and the optimal control problem for flight in the atmosphere is formulated. No approximations about the nature of the trajectory are made, so that the results are fully optimal for the planet model used. As an example of the use of the optimal formulation obtained, the problem of maximum lateral range of a vehicle returning to earth from orbit is solved.; The problem of optimal aerodynamic plane rotation for all entry speeds and plane change angles is solved and the behavior of the state and control variables is displayed and analyzed. Upon combining with propulsive maneuvers in the vacuum, the aeroassisted transfer modes from high circular orbit to low circular orbit are obtained. The combined maneuver is optimized so that the results are globally optimal. Several optimal modes of transfer are found which had not been previously considered. It is shown that for most practical transfers from high to low circular orbits, an aeroassisted transfer is substantially more fuel optimal than a pure propulsive transfer. |
