Attitude translation coupling in a rotating drag-free satellite

The translational and attitude control of a drag-free, rotating satellite are usually designed to be independent of each other. However, coupling may exist which can produce instability. The different types of coupling and the stability conditions are studied, using root locus type techniques. The resulting root loci have unusual shapes due to the nonlinearity of the characteristic polynomial in terms of the coupling parameters. It is possible, however, to use standard root loci techniques by appropriate factoring and subsequent superposition of loci. The effect of the main parameters upon the overall stability of the system is studied. Both, attitude and translation instabilities eventually arise - the former being more critical for typical satellite designs. An analytical expression for the stability boundary is developed.