Stability of the elliptically excited pendulum using the homoclinic melnikov function

Richard A. Morrison*, Marian Wiercigroch

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we investigate the dynamics of a pendulum subject to an elliptical pattern of excitation. The physical model is motivated by the development of sea wave energy extraction systems which exploit the rotating solutions of pendulum systems to drive generation. We formulate the homoclinic Melnikov function for the system and then demonstrate bounds on the set of parameters which can support homoclinic bifurcation. As the homoclinic bifurcation is a precursor to escape and the formation of rotating solutions in the evolution of the system under increasing forcing, these estimates provide bounds on the parameter space outwith which stable rotating solutions are not observed.

Original languageEnglish
Title of host publicationIUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design - Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design
EditorsMarian Wiercigroch, Giuseppe Rega
PublisherSpringer Verlag
Pages87-94
Number of pages8
ISBN (Print)9789400757417
DOIs
Publication statusPublished - 1 Jan 2013
EventIUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, 2010 - Aberdeen, United Kingdom
Duration: 27 Jul 201030 Jul 2010

Publication series

NameIUTAM Bookseries
Volume32
ISSN (Print)1875-3507

Conference

ConferenceIUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, 2010
CountryUnited Kingdom
CityAberdeen
Period27/07/1030/07/10

Keywords

  • Elliptically excited pendulum
  • Homoclinic melnikov function
  • Rotating solutions

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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  • Cite this

    Morrison, R. A., & Wiercigroch, M. (2013). Stability of the elliptically excited pendulum using the homoclinic melnikov function. In M. Wiercigroch, & G. Rega (Eds.), IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design - Proceedings of the IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design (pp. 87-94). (IUTAM Bookseries; Vol. 32). Springer Verlag. https://doi.org/10.1007/978-94-007-5742-4_7