Attitude Stability of DeBra-Delp Satellites in Circular Orbit

Abstract

DeBra‐Delp satellite refers to a particular attitude with respect to the orbital coordinates of certain rigid threeaxis satellites. The attitude stability of such a satellite placed on a circular orbit, examples of which can be found among natural and artie cial satellites, is examined. As is well known, linearized techniques for the stability of the particular equilibrium of the named satellites have been inconclusive because no Lyapunov function for them was found. Our aim is to demarcate a region in the parameter space (T1;T2) dee ned by the moments of inertia, where theequilibrium of DeBra-Delp satellitesisstable. Thisaim is achieved using and contrasting both analytical and numerical solutions and analyzing nonlinear characteristics of the problem. The analytical approach used is based on Tkhai’ s theorem, which represents an extension of the KAM theory and provides a sufe cient criterion for stability.