  Single-loop elastic rings can be folded into multi-loop equilibrium
configurations. In this paper, the stability of several such multi-loop states
which are either circular or straight are investigated analytically and
illustrated by experimental demonstrations. The analysis ascertains stability
by exploring variations of the elastic energy of the rings for admissible
deformations in the vicinity of the equilibrium state. The approach employed is
the conventional stability analysis for elastic conservative systems which
differs from most of the analyses that have been published on this class of
problems, as will be illustrated by reproducing and elaborating on several
problems in the literature. In addition to providing solutions to two basic
problems, the paper analyses and demonstrates the stability of six-sided rings
that fold into straight configurations.
