Quasilinearization determination of optimum finite-thrust orbital transfers.

Abstract

Quasilinearization was utilized to solve a discontinuous two-point boundary-value problem that resulted from a variational formulation concerning optimal orbital transfer. The boundary conditions were such that the transfer trajectory's endpoints could be assumed to be at unspecified positions upon arbitrary coplanar orbits. The vehicle was assumed to be thrustlimited and capable of controlling thrust direction and duration (bang-bang throttle control). Through careful use of the quasilinearization technique, it was possible to determine trajectories that minimized the fuel required for orbital transfer maneuvers that were accomplished in a fixed time interval. It was found that accurate initial conditions, which were derived from the corresponding optimal impulsive orbital transfers, were required for convergence of the quasilinearization process. An IBM 7094 double-precision computer program incorporating the aforementioned techniques then was utilized to generate optimal transfers between numerous pairs of arbitrary coplanar orbits. Using the resulting data, it was possible to make a series of significant comparisons concerning the velocity changes required for corresponding optimal finite-thrust and optimal impulsive orbital transfers. Further numerical investigations demonstrated the existence of optimal transfers between shallowly intersecting orbits that required only one thrusting period. These maneuvers were shown to be analogous to the better known optimal one-impulse maneuver.