Axially excited spatial double pendulum nonlinear dynamics.

Abstract

Analysis of a 3D spatial double physical pendulum system, coupled by two universal joints is performed. External excitation of the mechanism is realized by axial periodic rotations of the first joint of the pendulum. System of ODEs is solved numerically and obtained data are analyzed by a standard approach, including time series, phase plots and Poincaré sections. Additionally, FFT (Fast Fourier Transform and the wavelet transformation algorithms have been applied. Various wavelet basic functions have been compared to find the best fit, e.g. Morlet, Mexican Hat and Gabor wavelets. The so far obtained results allowed for detection of a number of non-linear effects, including chaos, quasi-periodic and periodic dynamics, as well the numerous and different bifurcations. Scenarios of transition from regular to chaotic dynamics have been also illustrated and studied.