On the determination of the asymptotic behavior of an inertially-oriented space station

In this paper some generalizations of the Lyapunov stability theory made by Yoshizawa and LaSalle are used to determine the asymptotic behavior of the motion relative to a three axis limit cycle of an inertially-oriented space station acted on by gravity gradient and aerodynamic torques and controlled by reaction jet thrusters. Although the uncontrolled system is unstable and the controller is bounded, it is shown that any trajectory with initial condition in a bounded set
G
will approach a subset
E \subset G
. It is shown that the subset
E
is small enough and
G
large enough to be practical for the particular spacecraft application.