In this paper, a system of the gyroscopes coupled via the massless torsional springs and the massless torsional dampers mounted on the tip mass of a column subjected to a vibrating base is considered. The coupled gyroscopes are assumed to have reverse angular speeds, and the rotations to eliminate the torques due to the springs and the dampers. Taking advantage of the angular momentum of the rotating gyroscope, gyrostabilizer systems are expected to become more widely actualized as they provide an effective means of motion control with several significant advantages for various structures. The non-linear motions of the gyro-column system and the equations of motion for the system are derived following energy (Lagrange) based approaches and examples provided. On the other hand, the effect of the angular velocities of the gyroscopes are studied, and it is shown that the angular velocity (spin velocity) of a gyroscope has a significant effect on the behavior of the dynamic motion. It is also shown how the dampers and springs due to the motion between the suporting gimbals influence the dynamic behavior of the column. (C) 2015 The Authors. Published by Elsevier Ltd.