Stability of an equilibrium solution for a gyrostat about an oscillating point

In the present paper will study the stability of an equilibrium solution of the problem of motion of a symmetric gyrostat about a point belonging to its rigid part when this point deecribes an oscillatory motion with amplitude z0 and frequency ω.Two systems of reference are considered: a system OXYZ, whose axes are parallel to those of a fixed or inertial frame and another mobile Oxyz, fixed in the body, and whose axes are directed along the principal axes of inertia of the gyrostat.