Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Grzegorz Litak*, Jerzy Margielewicz, Damian Gąska, Daniil Yurchenko, Krzysztof Dąbek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
102 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)2125-2142
Number of pages18
JournalNonlinear Dynamics
Issue number4
Early online date18 Nov 2020
Publication statusPublished - Dec 2020


  • Amplitude–frequency spectrum
  • Chaos
  • Lissajous curves
  • Lyapunov exponents
  • Nonlinear oscillations
  • Spherical pendulum
  • Strange attractor

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation'. Together they form a unique fingerprint.

Cite this