General Formulation of Powered Flight Trajectory Optimization Problems

Abstract

A general formalism, applicable to a wide class of missile trajectory optimization problems, is obtained by straightforward application of standard methods of the calculus of variations. In all cases, a point particle model is used for the missile. It is shown that the steering and burning programs are determined always by the same differential equations, different optimization problems corresponding simply to different boundary conditions. Results found previously by assuming the gravitational force field uniform during powered flight are obtained as special cases and the corrections to these due to variations in the force field are discussed. The extensions to variable mass and thrust programs, variable burning times, etc., are also included.