Dynamics of spinning bodies containing liquid

Liquids can have a considerable influence on the dynamics of spinning satellites, in particular they can turn a system unstable. To study this effect, the linearized partial and ordinary differential equations including border conditions are established and solved. It turns out that two sorts of stability limits do exist, one for the damped and one for the undamped system. Stability diagrams for both types of systems are given in the parameter plane. They include the solutions of special cases reported in the literature.