Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation
Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation
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.
Nonlinear oscillations, Spherical pendulum, Strange attractor, Chaos, Lyapunov exponents, Lissajous curves, Amplitude–, frequency spectrum
2125-2142
Litak, Grzegorz
03a00531-56de-4e58-9aa7-d8018491262c
Margielewicz, Jerzy
a71daea3-a922-4129-949c-9d34c5e7a3e2
Gaska, Damian
1fadc103-4b7e-4338-9543-f87c7ce5c54e
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
Dabek, Krzysztof
48f25a8c-25ea-472c-bb88-44f013d1e959
1 December 2020
Litak, Grzegorz
03a00531-56de-4e58-9aa7-d8018491262c
Margielewicz, Jerzy
a71daea3-a922-4129-949c-9d34c5e7a3e2
Gaska, Damian
1fadc103-4b7e-4338-9543-f87c7ce5c54e
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
Dabek, Krzysztof
48f25a8c-25ea-472c-bb88-44f013d1e959
Litak, Grzegorz, Margielewicz, Jerzy, Gaska, Damian, Yurchenko, Daniil and Dabek, Krzysztof
(2020)
Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation.
Nonlinear Dynamics, 102 (4), .
(doi:10.1007/s11071-020-06023-5).
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.
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More information
Accepted/In Press date: 12 October 2020
e-pub ahead of print date: 18 November 2020
Published date: 1 December 2020
Keywords:
Nonlinear oscillations, Spherical pendulum, Strange attractor, Chaos, Lyapunov exponents, Lissajous curves, Amplitude–, frequency spectrum
Identifiers
Local EPrints ID: 469670
URI: http://eprints.soton.ac.uk/id/eprint/469670
ISSN: 0924-090X
PURE UUID: 7effc5c5-fcc5-43d0-9131-f9dc5d3c0ea1
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Date deposited: 21 Sep 2022 17:08
Last modified: 17 Mar 2024 04:11
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Contributors
Author:
Grzegorz Litak
Author:
Jerzy Margielewicz
Author:
Damian Gaska
Author:
Daniil Yurchenko
Author:
Krzysztof Dabek
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