Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
- 1 June 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in European Journal of Applied Mathematics
- Vol. 3 (2) , 97-114
- https://doi.org/10.1017/s0956792500000735
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.Keywords
This publication has 9 references indexed in Scilit:
- Global uniqueness of homoclinic orbits for a class of fourth order equationsZeitschrift für angewandte Mathematik und Physik, 1992
- Localized buckling in long axially-loaded cylindrical shellsJournal of the Mechanics and Physics of Solids, 1991
- Comparative lagrangian formulations for localized bucklingProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991
- First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systemsMathematische Annalen, 1990
- Structural localization phenomena and the dynamical phase-space analogyProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1989
- Existence of symmetric homoclinic orbits for systems of Euler-Langrange equationsProceedings of Symposia in Pure Mathematics, 1986
- A global branch of solutions to a semilinear equation on an unbounded intervalProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1985
- Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systemsMathematische Annalen, 1984
- Some global results for nonlinear eigenvalue problemsJournal of Functional Analysis, 1971