Stability and Control in Space Craft Dynamics

Abstract

. An optimal control problem for the spacecraft dynamics is discussed and some of its properties are pointed out. 1. Introduction Recent work in nonlinear control has drawn attention to drift--free systems with fewer controls than state variables. These arise in problems of motion planning for wheeled robots subject to nonholonomic controls [12], [13], models of kinematic drift effects in space systems subject to appendage vibrations or articulations [5], [6], models of self-propulsion of paramecia at low Reynolds numbers [16] and autonomous underwater vehicle dynamics [8]. The goal of our paper is to discuss a similar problem for the spacecraft dynamics. The case with drift can be found in [11]. 2. The spacecraft as a drift-free left invariant system on SO(3) Let us consider a spacecraft free to move in R 3 . Let (b 1 ; b 2 ; b 3 ) be an orthonormal frame fixed on the body and let (r 1 ; r 2 ; r 3 ) define an inertial frame with the origin coincident with the origin of the body-fi...