Dynamical equilibrium stability of heavy rotating filament in contour motion

Dynamic equilibrium of absolutely flexible unstretchable rotating heavy filament, that makes a contour motion along the line of apparent rest, is investigated. With allowance made for gravity force as well as for moving, relative and Coriolis inertial forces, the transition from plane forms of motion to spatial ones is studied depending on velocity of contour motion and angular velocity of system rotation. The critical values of magnitudes are found at which the dynamic equilibrium ceases to be stable.