Optimality of intermediate-thrust arcs of rocket trajectories

Abstract

A new necessary condition is derived for the optimality of intermediate-thrust arcs of rocket trajectories in vacuum. The new necessary condition, together with previously known necessary conditions, ensures the absolute optimality of sufficiently short intermediatethrust arcs. For inverse-square central fields, the new condition reduces to a requirement that the primer vector must point inward; its radial component must be negative. Intermediate-thrust arcs that satisfy the new condition cannot join to arcs of a finite maximum thrust, nor join directly (without impulses) to arcs of zero thrust, except in a very restricted set of special cases. They are, therefore, of theoretical rather than practical importance.