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

Published online by Cambridge University Press:  16 July 2009

C. J. Amick  and
J. F. Toland
C. J. Amick
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
J. F. Toland
Affiliation:
School of Mathematical Sciences, University of Bath Claverton Down, Bath BA2 7AY, UK
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Abstract

The equation

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 of (*), 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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 2 , June 1992 , pp. 97 - 114
Copyright
Copyright © Cambridge University Press 1992

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