We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show...

The bistablity onset due to the interaction of highto low-frequency oscillations in the Duffing oscillator is considered. It is shown that such interaction results in arising of additional bistable states, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the harmonically forced oscillator. This phenomenon is illustrated by considering two examples...

Abstract We investigate the dynamics of two quantum mechanical oscillator system–bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled a massive scalar field and electrodynamics (QED). The scalar-gravity model maps onto phase damped oscillator, while QED approximately an system subject two-photon damping. provide potentially useful insights into solving fo...

This paper considers near time-optimal setpoint tracking of a second-order oscillator. First, the time-optimal setpoint tracking feedback law is derived by recasting the problem as a regulator problem in the error coordinates with shifted control limits. This result is used to construct a derated approximation of the optimal control, PTOSω. Initially, the PTOSω is derived for a regulator contro...