A nonvariational approach to multiple finite-burn propellant optimization

In this paper a nonvariational approach to the finite-burn minimum fuel problem is presented. In particular, attention is focused on one of the computer codes of a sophisticated software package at Telespazio for dealing with a fuel minimization under nonlinear equality and inequality constraints. In this program thrust in an inverse-square gravitational field is considered. A short thrusting arc is dealt with by a transition matrix. A long burning arc is segmented in a suitable number of subarcs where the transition matrix formulation holds. Use of appropriate penalty functions allows the mission analyst to consider several equality and inequality constraints. The minimum search algorithm consists of a modified version of the Levenberg-Marquardt method. The overall computer code is able to accept even some rough estimate of the optimal profile. A wide spectrum of transfer flights is presented.