Stability and self-oscillations of a rotor containing a conducting liquid in a magnetic field

This paper considers the problem of the stability in the small of the steady-state spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the butt-end boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was $D$-partitioned into regions with different degrees of instability is constructed. Steady-state spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steady-state spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steady-state spinning can be subcritical or supercritical.