Optimal transfer between elliptic orbits with three tangential impulses

This paper introduces a mathematical model that can be used to evaluate the total velocity variation required to accomplish a given two-dimensional orbit transfer, using up to three tangential impulsive maneuvers. The problem is addressed in an optimal framework, by looking for the transfer trajectory that minimizes the total velocity variation. In particular, by exploiting the boundary nonlinear constraint equations, the total velocity variation can be calculated as a function only of the spacecraft angular position at which the impulses are applied. The small number of control variables involved in the algorithm allows the optimization problem to be solved in a simple and robust way, with a small computational effort. The algorithm is able to find the optimal transfer strategy in a generic ellipse-to-ellipse, two-dimensional, mission scenario.