Partially filled nutation damper for a freely precessing gyroscope

Abstract

Transient responses of a freely processing gyroscope carrying a partially filled mercury ring damper are analyzed. An eccentric annulus is proposed to model the experimentally observed shape of the mercury, which is considered as deformable continuum. The variables describing the position of the center of mass of this continuum are defined as generalized coordinates. The frictional force between the mercury and the wall of the damper is derived in terms of the variables defining the free surface of the mercury and their time derivatives. Coupled equations of motion of the mercury and the rotor are derived by Lagrange's method in the form of ordinary differential equations rather than partial differential equations. These equations are employed in analyzing the effects of the parameters of the damper on the decay time constant of the nutation angle. The number of rings in the damper and the amount of mercury in each ring both have significant influence on the decay time constant. The theoretically predicted decay time constant is verified by experiment.