THE STABILITY OF THE CYLINDRICAL PRECESSION OF A VISCOELASTIC BODY UNDERGOING OSCILLATIONS ALONG AN AXIS OF SYMMETRY

The relative motion of a viscoelastic body undergoing longitudinal oscillations along an axis of symmetry in a Newtonian central gravitational field is considered. The linear theory of viscoelasticity is used. The stability of a particular solution of the equations of motion is studied. This solution corresponds to the uniform rotation of the body about an axis of symmetry perpendicular to the plane of the circular orbit. Using the reduction principle of the theory of denumerable systems of differential equations and Kamenkov's criterion, the stability in the whole domain of variation of the parameters in the non-linear problem is investigated. It is shown that the ''quasi-static approach'' to studying stability is correct.