Mechanical manifestations of bursting oscillations in slowly rotating systems

This study is concerned with certain mechanical systems that comprise discrete masses moving along slowly rotating objects. The corresponding equation of relative motion is derived, with the rotating motion creating slowly varying external excitation. Depending on the system parameters, two cases are distinguished: two-well and single-well potential, i.e. the Duffing bistable oscillator and a pure cubic oscillator. It is illustrated that both systems can exhibit bursting oscillations, consisting of fast oscillations around the slow flow. Their mechanisms are explained in terms of bifurcation theory: the first one with respect to the existence of certain saddle-node bifurcation points, and the second one by creation of a certain hysteresis loop. The exact expressions for the slow flow are derived, in the first case as a discontinuous curve, and in the second one as a continuous curve. The influence of the excitation magnitude, which is a potential control parameter, on the characteristics of bursting oscillations is numerically illustrated.