An investigation of optimal rocket flight in the vicinity of a planet

Abstract

Some problems of optimal thrust magnitude and thrust direction control for a rocket vehicle maneuver in a vacuum in the vicinity of a spherical planet are considered. The paper consists of three sections.

In Section I the problem of optimum thrust magnitude and thrust direction programming for a rocket travelling in a central gravitational field is investigated. It is shown that for the optimal motion in a rather near vicinity of a planet there exists the control plane, i.e., the optimum thrust vector lies in a plane with constant orientation in the inertial (Galilei) reference system. In other words, the existence of an invariant direction with a zero optimal thrust vector projection on it is proved.

In Section II a family of approximate analytical solutions for the problem of optimal transfer between near circular orbits with low thrust engine and ideal exhaust velocity control is studied. Some results on transfer control synthesis (with full information) are given.

In Section III a numerical analysis of a vehicle optimal landing problem (in the sense of propellant expenditure) at a predicted impact-point on the Lunar surface is made. Planar descent trajectories of a vehicle from low-altitude selenocentric orbits in a central gravitational field are studied. The optimal thrust direction and thrust magnitude programs are found. The influence of some parameters (thrust-weight ratio, the altitude of the initial satellite orbit, range angle of a descent) on mass expenditure is considered. A similar problem is solved for the putting of Lunar vehicle into a Moon satellite orbit.

Sections I and III are written by V.K. Isaev and B. Kh. Davidson, Section II is written by V.K. Isaev and V.V. Sonin.