ANALYTIC SOLUTIONS FOR INTERMEDIATE-THRUST ARCS OF ROCKET TRAJECTORIES IN A NEWTONIAN FIELD

Mayer's variational problem of determining the optimum trajectories of a rocket moving with constant exhaust velocity and bounded mass how r ate in a Newtonian field is considered. New analytic solutions are obt ained for plane intermediate-thrust arcs, using the canonical system o f equations of the variational problem and the properties of the switc hing function. These solutions represent certain spiral trajectories. In motion with a fixed time, at arbitrary angular distances, these sol utions satisfy Robbins' necessary optimum condition. As an example the problem of minimizing the characteristic velocity of flight between e lliptic orbits is considered. Copyright (C) 1996 Elsevier Science Ltd.