  A large family of deployable filamentary structures can be built by
connecting two elastic rods along their length. The resulting structure has
interesting shapes that can be stabilized by tuning the material properties of
each rod. To model this structure and study its stability, we show that the
equilibrium equations describing unloaded states can be derived from a
variational principle. We then use a novel geometric method to study the
stability of the resulting equilibria. As an example we apply the theory to
establish the stability of all possible equilibria of the Bristol ladder.
