On the steady motions op a gyrostat satellite: PMM vol. 33, no. 1, 1969, pp. 127–131

Abstract

Two families of steady motions of a gyrostat satellite in a central Newtonian force field are considered. The plane of the (circular) orbit of the center of mass of the satelite is biased relative to the attracting center. Sufficient conditions for stability are derived. These motions complement the numerous already familiar [1] steady motions of a gyrostat satellite with the center of the circular orbit coincident with the attracting center. As in the case of the latter motions, the stability conditions in our case differ from those obtained under the restricted formulation of the problem [1] by quantities on the order of l 2/R 2 relative to the principal terms ( l is the characteristic dimension of the satellite, R is the distance from the attracting center). The orbital plane bias is of the order of l 2/R 2 . These quantities are very small indeed when one is dealing with real artificial earth satillites. The present study is carried out by the Routh method with the aid of some results obtained by Rumiantsev [1].