Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
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