Design of a viscous ring nutation damper for a freely precessing body

A ring damper partially filled with mercury for removing the wobble motion of a freely precessing body is analyzed. Coupled equations of motion of the rotor and mercury are derived in terms of Euler parameters and quasi-coordinates for the purposes of computational efficiency and singularity-free solution when the nutation angle approaches zero. An experiment is made to verify the theoretical solution of the nutation angle obtained by numerical integration of the equations of motion. The best choice of parameters of the damper is obtained by solving a minimum-time optimization problem that minimizes the time elapsed in the nutation-synchronous mode as well as the residual nutation angle in the spin-synchronous mode. The results show that the decay of the nutation angle can be accelerated to a great extent if the damper is properly designed. (Author)