This article is cited in 3 papers

Existence of energy minimums for thin elastic rods in static helical configurations

M. Argeri^a, V. Barone^b, S. De Lillo^c, G. Lupo^c, M. Sommacal<sup>c

a</sup> Università degli Studi di Napoli Federico II
^b Scuola Normale Superiore in Pisa
^c Dipartimento di Matematica e Informatica, Universita degli Studi di Perugia

Abstract: We characterize families of solutions of the static Kirchhoff model of a thin elastic rod physically. These families, which are proved to exist, depend on the behavior of the so-called register and also on the radius and pitch. We describe the energy densities for each of the solutions in terms of the elastic properties and geometric shape of the unstrained rod, which allows determining the selection mechanism for thepreferred helical configurations. This analysis promises to be a fundamental tool for understanding the close connection between the study of elastic deformations in thin rods and coarse-grained models with widespread applications in the natural sciences.

Keywords: thin elastic rod, Kirchhoff equation, inverse problem, integrability, helix.

DOI: 10.4213/tmf6354

 English version: Theoretical and Mathematical Physics, 2009, 159:3, 698–711

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