Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends

The paper addresses the stability problem of curvilinear configurations of a perfectly flexible rod known as elasticas. The question of stability of equilibrium configurations is reduced to investigating the sign of the energy functional in the presence of isoperimetric constraints. It is shown that the associated Jacobi equation can be integrated analytically, which makes it possible to perform the stability analysis for the rod equilibrium configurations using exact closed-form solutions expressed in terms of elliptic functions. The classical problem of a clamped–clamped rod is considered and complemented by the stability analysis.