The problem of finding the regions of instability of a system with a periodically varying moment of inertia 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
