1. Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation
- Author
-
Krzysztof Dąbek, Grzegorz Litak, Damian Gąska, Jerzy Margielewicz, and Daniil Yurchenko
- Subjects
Physics ,Applied Mathematics ,Mechanical Engineering ,Spherical pendulum ,Mathematical analysis ,Aerospace Engineering ,Ocean Engineering ,Lyapunov exponent ,Horizontal plane ,Bifurcation diagram ,01 natural sciences ,law.invention ,010101 applied mathematics ,Lissajous curve ,symbols.namesake ,Control and Systems Engineering ,law ,0103 physical sciences ,Attractor ,symbols ,Cartesian coordinate system ,0101 mathematics ,Electrical and Electronic Engineering ,Nonlinear Oscillations ,010301 acoustics - Abstract
This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.
- Published
- 2020