## 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.

Original language | English |
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Pages (from-to) | 2125-2142 |

Number of pages | 18 |

Journal | Nonlinear Dynamics |

Volume | 102 |

Issue number | 4 |

Early online date | 18 Nov 2020 |

DOIs | |

Publication status | Published - Dec 2020 |

## Keywords

- 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