ON MOTION OF A SYMMETRICAL GYROSTAT IN A NEWTONIAN FORCE-FIELD

A spherical cavity in a sphere-shaped gyrostat contains a spherical ro tor, which is rotating at a constant angular velocity relative to the outer sphere. The centres of the outer sphere, the cavity and the roto r coincide. Attached to the outer sphere are identical point masses, p laced at the vertices of an octahedron. A study is presented of the in fluence of the rotation of the rotor an 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 wh ich 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. (C) 1998 Elsevier Science Ltd. ALL rights reserved.