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  • European Journal of Applied Mathematics, Volume 3, Issue 2
  • June 1992, pp. 97-114

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

  • C. J. Amick (a1) and J. F. Toland (a2)
  • DOI: http://dx.doi.org/10.1017/S0956792500000735
  • Published online: 01 July 2009
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

H. Hofer & J. F. Toland 1984 Homoclinic heteroclinic and periodic orbits for a class of indefinite Hamiltonian systems. Math. Annalen 268, 387403.

H. Hofer & K. Wysocki 1990 First order elliptic systems and the existence of homoclinic orbits in Hamilionian systems. Math. Annalen 288, 483503.

G. W. Hunt , H. M. Bolt & J. M. T. Thompson 1989 Localisation and the dynamic phase-space analogy. Proc. Roy. Soc. Lond. A 425, 245267.

G. W. Hunt & M. K. Wadee 1991 Comparative Lagrangian formulations for localized buckling. Proc. Roy. Soc. Lond. A 434, 485502.

G. W. Hunt & Neto E. Lucena 1991 Localized buckling in long axially-loaded cylindrical shells. J. Math. Phys. Solids 39, 881894.

P. H. Rabinowitz 1971 Some global results for nonlinear eigenvalue problems. Journal Fnal. Anal. 7, 487513.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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