Mt. Aygun et U. Daybelge, ATTITUDE STABILITY OF DEBRA-DELP SATELLITES IN CIRCULAR ORBIT, Journal of guidance, control, and dynamics, 21(6), 1998, pp. 965-970
DeBra-Delp satellite refers to a particular attitude with respect to t
he orbital coordinates of certain rigid three-axis satellites. The att
itude stability of such a satellite placed on a circular orbit, exampl
es of which can be found among natural and artificial satellites, is e
xamined. As is well known, linearized techniques for the stability of
the particular equilibrium of the named satellites have been inconclus
ive because no Lyapunov function for them was found. Our aim is to dem
arcate a region in the parameter space (T-1, T-2) defined by the momen
ts of inertia, where the equilibrium of DeBra-Delp satellites is stabl
e. This aim is achieved using and contrasting both analytical and nume
rical solutions and analyzing nonlinear characteristics of the problem
. The analytical approach used is based on Tkhai's theorem, which repr
esents an extension of the KAM theory and provides a sufficient criter
ion for stability.