Numerical Investigation of Minimum Impulse Orbital Transfer

A method for the precise numerical determination of optimum two-impulse orbital transfers between inclined elliptical orbits is described. A numerical optimization technique termed "adaptive steepest descent" is shown to overcome convergence difficulties encountered with other less powerful methods. A double-precision IBM 7094 program incorporating this technique was used to make detailed studies of complicated impulse function spaces associated with various orbit pairs which had been previously investigated by function contouring. Several interesting results, including the existence of at least three locally minimum two-impulse transfers between "almost tangent" coplanar elliptical orbits, were revealed by these numerical studies. Other numerical data indicates that minimum impulse transfer circumstances for coplanar orbits may be extended to strongly inclined orbits; that is, one and two-impulse maneuvers which are optimal exist for classes of inclined orbits. Results of a study of orbits which osculate to a Lawden Spiral are also presented. It was found that two-impulse transfers between these orbits always required less velocity change than a transfer between the points of osculation, along a Lawden Spiral. Extensive numerical comparison revealed that the difference in velocity change for the two maneuvers increases approximately as the 4.7 power of a parameter denoting distance between the points of osculation on the Lawden Spiral.