Optimal Interstellar Trajectories with Relativistic Rockets Using Combined Thrust and Acceleration Limited Control.

The purpose of this study was to investigate the characteristics of one-dimensional relativistic minimum time trajectories of single-stage rockets subject to both a thrust constraint and an acceleration constraint. Gravitational and drag forces are neglected. The rocket exhaust velocity is considered constant, and the maximum acceleration, as measured on the rocket, is about one g. The rocket starts from the origin of an inertial system at zero time velocity. The two-p0int boundary-value problem that satisfies the necessary conditions is set up using Pontryagins minimum principle. It is solved to provide the relativistic optimal control law for the minimum time trajectories. Assuming zero final velocity, the characteristics of the relativistic minimum time trajectories are determined. The results are compared with those for rockets subject to a thrust constraint only and rockets subject to an acceleration constraint only. Modified author abstract