Linear Boundary Port Hamiltonian Systems defined on Lagrangian submanifolds

Recently Port Hamiltonian systems have been extended to encompass an implicit definition of the energy function of the system, by defining it in terms of a Lagrangian submanifold. In this paper, we extend the definition of Port Hamiltonian systems defined with respect to Lagrangian submanifold to a class of infinite-dimensional systems where the Lagrangian submanifold is defined by first-order differential operators. We show that this adds some port boundary variables and derive the energy balance equation. This construction is illustrated on the model of a flexible nanorod made of composite material.