An elastica is a mathematical model of a beam undergoing the large deformations and rotations. The central line of beam is assumed to be inextensible in order to make the analysis of the beam feasible. Since the extensional deformation is not included in the strain energy of beam, the variational theory for the inextensible elastica has not been developed. In the present paper, the principle of virtual work and the principle of stationary potential energy for the elastica, exclusively expressed in terms of bending deformations, are derived from the principle of virtual work in the three dimensional elasticity. And it is shown that the developed variational principles yield the exact equilibrium equations for the beam in the large deformations and rotations.
