Dynamical and secular instability of a homogenous self-gravitating rotating cylinder

The non-axisymmetric oscillations and stability of a homogeneous self-gravitating rotating cylinder are investigated. Two infinite discrete spectra of rotational modes arises. Dynamical and secular instability occur for wavelengths situated in a certain interval, if ²>(m – 1 )/2m where denotes the angular velocity andm the azimuthal wave-number. Modes of maximum instability and maximum growth rates are determined. Viscosity reduces the growth rate of smaller wavelengths but increases the instability of the longer wavelengths. We show that the onset of secular instability is associated with a point of neutral oscillation.