European Journal of Applied Mathematics

Research Article

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

C. J. Amicka1* and J. F. Tolanda2

a1 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA

a2 School of Mathematical Sciences, University of Bath Claverton Down, Bath BA2 7AY, UK


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.

(Received May 13 1991)


* R.I.P. 3rd June 1991.