THE LIPAUNOV STABILITY OF THE ROTATION OF A GYROSTAT

Abstract

First sufficient conditions (including equalities) of the stability and the instability of the rotation of a gyrostat in a uniform field are obtained by the Liapunov direct method. Next sufficient conditions (including equalities) of the stability and the instability of the rotation of a gyrostat in a Newtonian central force field are studied by the Liapunov direct method. In the third part, the instability of the rotation of a gyrostat both in a uniform field and in a central force field is studied by the first approximation theorem and the results are compared with those obtained from the Liapunov. direct method.