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2013 | OriginalPaper | Chapter

Stability of the Elliptically Excited Pendulum Using the Homoclinic Melnikov Function

Authors : Richard A. Morrison, Marian Wiercigroch

Published in: IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

Publisher: Springer Netherlands

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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.

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Metadata
Title
Stability of the Elliptically Excited Pendulum Using the Homoclinic Melnikov Function
Authors
Richard A. Morrison
Marian Wiercigroch
Copyright Year
2013
Publisher
Springer Netherlands
Book
IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design

Print ISBN: 978-94-007-5741-7

Electronic ISBN: 978-94-007-5742-4

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-94-007-5742-4_7

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