Stability of a rotor motion in a chamber filled with viscous gas

Two problems of motion and stability of a solid heavy cylinder in vertical and horizontal chambers filled with viscous gas are solved. In the first problem distribution of velocities and pressures in the layer between the cylinder and the chamber is determined analytically. Stability criteria of a rotating cylinder (a rotor) motion subject to problem parameters are studied. Then the problem of motion of a horizontal rotating rigid unstable cylinder in a stationary circular cylindrical chamber, which has finite length and is filled with viscous gas is solved. The inner cylinder is influenced by outer forces which vary periodically in time. Trajectories of the rotor stationary motion for various velocities of rotation, disbalance values, amplitudes and frequencies of outer forces are calculated. Conditions of contact free motion of the cylinder, rotating in the chamber, are determined.