Abstract
A spherical cavity in a sphere-shaped gyrostat contains a spherical rotor, which is rotating at a constant angular velocity relative to the outer sphere. The centres of the outer sphere, the cavity and the rotor coincide. Attached to the outer sphere are identical point masses, placed at the vertices of an octahedron. A study is presented of the influence of the rotation of the rotor on the existence and stability of steady motions of the gyrostat about its mass centre in the Newtonian field of a fixed attracting centre. Interest centres on motions in which the radius vector of the gyrostat centre and the gyrostatic moment are collinear. It is shown that the existence of a gyrostatic moment may essentially modify the stability properties of the steady motions discovered.
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