Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

• DOI: 10.1007/s11071-020-06023-5
• Publication Date: 2020-11-18T16:04:07Z
• Authors: Grzegorz Litak; Jerzy Margielewicz; Damian Gąska; Daniil Yurchenko; Krzysztof Dąbek
• Keywords: Lissajous curve; Pendulum; Horizontal plane; Inclined plane; Position (finance); Kapitza's pendulum; Phase plane

Abstract This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The has two degrees freedom: rotational angle defined in plane and an inclination by respect to vertical z axis. results numerical simulations are illustrated mathematical model form multi-colored maps largest Lyapunov exponent. graphical images geometrical structures attractors placed on Poincaré cross sections shown against resolution density trajectory points passing through control plane. Drawn for steady-state, tip mass three-dimensional space. obtained trajectories moving referred constructed bifurcation diagram.