Some optimal low-acceleration rendezvous maneuvers

Abstract

For each of three specific rendezvous missions, the low-acceleration piogram which optimizes performance, as referred to some figure of merit, is obtained Specifically, these figures of merit are either propellant or time, and each of the missions is pei formed in a manner that will minimize one of these quantities subject to suitable constraints Whenever possible, the differential equations of motion are integrated, with the use of the optimum acceleiation program, to obtain the trajectory of the vehicle(s) as an explicit function of time In general, the equations from which the desired optimal results are to be extracted are sufficiently complicated so that some machine computation is required The emphasis on such computation varies between the three solutions An illustrative example comparing an optimum acceleration program with an equivalent constant tangential acceleration program is included in the paper This comparison shows that the optimum program is slightly superior to the tangential program The magnitude and direction of the optimal acceleration vector is shown to vary The optimum low-acceleration programs are obtained by employing the technique of differential games A brief summary of the philosophy involved in this optimization procedure and a list of required equations are included for reference purposes