General theory of optimal trajectory for rocket flight in a resisting medium

Abstract

This paper considers the problem of optimizing the flight trajectory of a rocket vehicle moving in a resisting medium and in a general gravitational force field. General control laws for the lift, the bank angle, and the thrusting program are obtained in terms of the primer vector, the adjoint vector associated to the velocity vector. Additional relations for the case of variable thrusting and integrals of motion for flight at maximum lift-to-drag ratio and flight in a constant gravitational field are obtained.