Parametric Oscillations of the Kochin Oscillator with Dissipation

Abstract

The fundamental properties of parametrically excited oscillatory systems of the Kochin oscillator type with double degeneracy of frequencies are investigated. The qualitative phenomenon of their absence is established for arbitrarily small actions of a dissipative nature. As a result, the resonance motions of the first mode prove to be relatively more substantial; the excitation of subsequent odd modes is difficult in the applied aspect and requires a significant increase in the eigenvalue of the corresponding parameter.