Nonlinear dynamical theory of the elastica

Russel Caflisch

Research output: Contribution to journalArticle

Abstract

The dynamical behaviour of a slender rod is analyzed here in terms of a generalization of Euler's elastica theory. The model includes a linear stress-strain relation but nonlinear geometric terms. Properties of the rod may vary along its length and various boundary conditions are considered. A rotational inertia term that is neglected in many theories is retained, and is essential to the analysis. By use of the equivalence of an energy and a Sobolev norm, and by reformulation of the equations as a semilinear system, global existence of solutions is proved for any smooth initial data. Equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to Liapounov.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume99
Issue number1-2
DOIs
StatePublished - 1984

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Elastica
Semilinear Systems
Equilibrium Solution
Term
Energy
Reformulation
Dynamical Behavior
Inertia
Global Existence
Euler
Existence of Solutions
Equivalence
Vary
Norm
Boundary conditions
Model
Generalization

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear dynamical theory of the elastica. / Caflisch, Russel.

In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 99, No. 1-2, 1984, p. 1-23.

Research output: Contribution to journalArticle

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