Integrals of the Motion for Optimal Trajectories in Atmospheric Flight

Abstract

The problem of optimizing the flight trajectory of a rocket vehicle moving in a resisting medium, in a general gravitational force field, is considered. Optimal laws for the modulation of the aerodynamic and propulsive forces are formulated in terms of the primer vector, the vector adjoint to the velocity. Relations for flight along an intermediate-thrust arc and integrals of the motion for several cases of practical interest are derived.