Extremal rocket motion with maximum thrust in a linear central field

摘要

The Mayer variational problem of determining optimal trajectories of a rocket moving with maximum thrust in a thin spherical layer within a central Newtonian field is considered. The present work is devoted to the analytical investigation of maximum thrust arcs for a rocket engine with constant exhaust velocity and limited mass flow rate using the necessary conditions of optimality. Many problems of practical interest admit an approximation of the central Newtonian field by a linear central field. It is shown that the linear central field assumption is valid when the thrust vector is nearly tangential to the orbit and the rocket remains in a sufficiently thin spherical layer during the maneuver. When the linear central field approximation is utilized, analytic closed-form expressions are obtained describing optimal maximum thrust space trajectories. The problem of optimal orbit transfer between coplanar circular orbits is considered to illustrate the solution process, which comprises two maximum thrust and three null thrust arcs. It is shown that solutions of the problem are comparable with solutions based on assumptions of instantaneous changes in velocity, including the Hohmann transfer. References: 9