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.
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