Dynamics of the nearly parametric pendulum

B. Horton, J. Sieber, J. M. T. Thompson, M. Wiercigroch

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region of instability.
Original languageEnglish
Pages (from-to)436-442
Number of pages7
JournalInternational Journal of Non-Linear Mechanics
Volume46
Issue number2
Early online date20 Nov 2010
DOIs
Publication statusPublished - Mar 2011

Fingerprint

Pendulum
Pendulums
Ellipticity
Excitation
Bifurcation
Scenarios

Keywords

  • parametric resonance
  • symmetry breaking

Cite this

Dynamics of the nearly parametric pendulum. / Horton, B.; Sieber, J.; Thompson, J. M. T.; Wiercigroch, M.

In: International Journal of Non-Linear Mechanics, Vol. 46, No. 2, 03.2011, p. 436-442.

Research output: Contribution to journalArticle

Horton, B. ; Sieber, J. ; Thompson, J. M. T. ; Wiercigroch, M. / Dynamics of the nearly parametric pendulum. In: International Journal of Non-Linear Mechanics. 2011 ; Vol. 46, No. 2. pp. 436-442.
@article{b3323cefc67d446eae2e32bcb678863c,
title = "Dynamics of the nearly parametric pendulum",
abstract = "Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region of instability.",
keywords = "parametric resonance, symmetry breaking",
author = "B. Horton and J. Sieber and Thompson, {J. M. T.} and M. Wiercigroch",
year = "2011",
month = "3",
doi = "10.1016/j.ijnonlinmec.2010.11.003",
language = "English",
volume = "46",
pages = "436--442",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Limited",
number = "2",

}

TY - JOUR

T1 - Dynamics of the nearly parametric pendulum

AU - Horton, B.

AU - Sieber, J.

AU - Thompson, J. M. T.

AU - Wiercigroch, M.

PY - 2011/3

Y1 - 2011/3

N2 - Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region of instability.

AB - Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical parametric pendulum. The first finding is that the region in the parameter plane of amplitude and frequency of excitation where rotations are possible increases with the ellipticity. Second, the resonance tongues, which are the most characteristic feature of the classical bifurcation scenario of a parametrically driven pendulum, merge into a single region of instability.

KW - parametric resonance

KW - symmetry breaking

U2 - 10.1016/j.ijnonlinmec.2010.11.003

DO - 10.1016/j.ijnonlinmec.2010.11.003

M3 - Article

VL - 46

SP - 436

EP - 442

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 2

ER -