Multiple Equilibrium States of Slightly Extensible Elastic Strings

We consider the equilibrium states of elastic strings loaded transversely by their own weight. We are interested in the relation between the equilibrium states of inextensible strings and those of strings which are nonlinearly elastic and slightly extensible. The inextensible string has a unique concave equilibrium state while the concave equilibrium states of a nonlinearly elastic string come in pairs. In this paper we explore the relation between the two models. This revised version was published online in August 2006 with corrections to the Cover Date.