Abstract: The number, the angles of orientation and the stability in Rumyantsev-Movchan's sense of steady rotations of a symmetric gyroscope with a cavity completely filled with a uniform viscous liquid on a plane are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotation with two types of jumps are obtained. By taking account of the M2-damping owing to the moment of unavoid...