On the stability of a flexibly mounted rotating cylinder partially filled with liquid

Summary An investigation is made into the unstable behaviour of a rotor which is flexibly mounted with some damping and which is forced to rotate around its axis of symmetry with a constant angular velocity. The rotor is assumed to be partially filled with an ideal liquid. Assuming relative liquid motion in two dimensions a perturbation theory leads to an algebraic equation of the fourth degree from which information can be derived about unstable regions and the effect of the combined action of dissipative and gyroscopic forces.