Summary
Nonlinear oscillatory behavior is commonly described in terms of amplitudes, phases, and frequencies. Only in rare cases, these quantities are constant and can be readily obtained via Fourier transformation. In many measurements of, for example, ocean waves, mechanical systems, and biological systems, the amplitudes and frequencies vary slowly in time. In this presentation, the authors present a strategy to decompose measurements of nonlinear oscillations into oscillations with slowly varying amplitudes and frequencies. The amplitude and frequency variations reveal fundamental insights into the observed oscillations and can be leveraged to derive modulation equations. These equations can be used to predict the oscillatory behavior when small perturbations are added. The capabilities of the proposed methodology are demonstrated using measurements from a nonlinear mechanical oscillator experiment.
