Stationary and non-stationary oscillatory dynamics of the parametric pendulum
The nonlinear dynamics of a parametrically excited pendulum is addressed. The proposed analytical approach aims at describing the pendulum dynamics beyond the simplified regimes usually considered in literature, where stationary and small amplitude oscillations are assumed. Thus, by combining complexification and Limiting Phase Trajectory (LPT) concepts, both stationary and non-stationary dynamic regimes are considered in the neighborhood of the main parametric resonance, without any restriction on the pendulum oscillation amplitudes.