Optimal multiple-impulse satellite evasive maneuvers

Abstract

Minimum-fuel, impulsive solutions are obtained for the evasive maneuver of a satellite followed by a rendezvous with the original orbit station. The evasion distance and time are constrained. Both free and constrained final time cases are considered. Primer vector theory is used to obtain optimal solutions, which include threeimpulse solutions for an arbitrarily oriented evasion radius vector of a specified magnitude, and two-impulse free-return trajectories for certain specific evasion radius vectors. On some three-impulse solutions the primer vector indicates that the addition of a fourth impulse to the return trajectory will lower the fuel cost. Nomenclature A =3X3 coefficient matrix in CW equations, Eq. (2) B =3X3 coefficient matrix in CW equations, Eq. (3) D = determinant of the matrix N, Eq. (A6) H = Hamiltonian function, Eq. (B9) / = velocity-change cost of nominal three-impulse trajectory K = time interval between initial and midcourse impulse, tm ~ t0