Decision Procedure of Maximum Landing Area Applied Homotopy Method

Abstract

Optimal control theory is applied to a large number of trajectory designs in aerospace engineering. For example, a reusable spaceplane uses a trajectory to an orbit with minimum fuel or a non-powered aircraft is required to glide as far as possible. Optimal control theory provides the necessary conditions of optimal trajectory. The problem is defined as an two-point boundary value problem (TPBVP). There is, however, no solution for a TPBVP in some cases due to severe terminal conditions. This paper discusses on procedure to find the existence of solution in a TPBVP using homotopy method. Homotopy method is a numerical calculation in which a guessed solution changes continually to the exact solution with definite integration. There is no assumption such as linearization, thus the existence of solution is clearly shown in the numerical calculation and the exact solution is provide with finite numbers of calculation. This paper is an intermediate report that the procedure is applied to the maximum range for non-powered aircraft