The regions of instability of a system with a periodically varying moment of inertia

The problem of finding the regions of instability of a system with a periodically varying moment of intertia is considered. An equation is derived which describes small torsional oscillations of a system with periodic coefficients, which depend on four constant parameters, including damping. A method of investigating stability based on an analysis of the behaviour of Floquet multipliers is described. Analytical expressions are obtained for the regions of instability (parametric resonance) in parameter space. Numerical examples are given.