A nutational motion damper includes a damping body positioned and constrained by springs to slide on a guide plate having a surface oriented substantially perpendicular to the axis of rotation of a gyroscopic body by opposed spring members. The guide plate is attached to a relatively non-rotating body coupled to the rotating gyroscopic body to follow nutational motion. The springs define a rest position for the damping mass on the axis of rotation and also urge the damping body against the guide plate.