Homoclinic orbits in the dynamic phase-space analogy of an elastic strut

C. J. Amick, J. F. Toland

Research output: Contribution to journalArticle

Abstract

The equation [Fomula ommited] is a possible dimensionless version of a model for the configuration of a very long strut resting on a nonlinear elastic foundation with axial loading P. By seeking to establish the existence of homoclinic orbits connecting the zero equilibrium, now regarded as defining a four dimensional dynamical system, to itself one is pursuing the so-called ‘dynamical phase-space analogy’ for the spatial configuration suggested by the form of the equation. The existence of homoclinic solutions is then interpreted as indicating the presence of spatially localized buckling of the deformed strut.

Original languageEnglish
Pages (from-to)97-114
Number of pages18
JournalEuropean Journal of Applied Mathematics
Volume3
Issue number2
DOIs
Publication statusPublished - Jun 1992

ASJC Scopus subject areas

  • Applied Mathematics

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