Classification of the spatial equilibria of the clamped elastica: numerical continuation of the solution set

We consider equilibrium configurations of inextensible, unshearable, isotropic, uniform
and naturally straight and prismatic rods when subject to end loads and clamped boundary conditions. In a first paper [NH02], we discussed symmetry properties of the equilibrium configurations of the centre line of the rod. Here we are interested in the set of all parameter values that yield equilibrium configurations that fulfill clamped boundary conditions. We call this set the solution manifold and we compute it using a recently introduced continuation algorithm. We then describe the topology of this manifold and how it comprises different interconnected layers. We show that the border set of the dierent layers is the well known solution set of buckled rings.