About the structure of the discrete and continuous Eringen’s nonlocal elastica

The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find variational integrating factor which enables us to provide and Hamiltonian structure associated equation. Explicit expressions of the solutions in terms elliptic integrals first kind are then deduced. We derive discrete version preserving compare it with Challamel’s co-worker definition elastica.