On stability of the Hill's equation with damping - Cattani, C.; Grebenikov, E.A.; Prokopenya, A.N. (Нелінійні коливання, 2004)
We consider the Hill’s equation with damping describing the parametric oscillations of the torsional pendulum excited by means of varying the moment of inertia of the rotating body. Using the method of a small parameter we have calculated analytically a fundamental system of solutions of this equation in the form of power series in the excitation amplitude ε with accuracy O(ε²) and verified the conditions of its stability. In the first-order approximation in ε, we have proved that the resonance domain exists only if the excitation frequency Ω is sufficiently close to the double natural frequency of the pendulum, and the corresponding equation of the stability boundary has been obtained.