Analysis and Comparison of Port-Hamiltonian Formulations for Field   Theories - demonstrated by means of the Mindlin plate
  This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a port-Hamiltonian setting, where we compare the approach based on Stokes-Dirac structures to a Hamiltonian setting that makes use of the involved bundle structure similar to the one on which the variational approach is based. We will use the Mindlin plate, a distributed parameter system with spatial domain of dimension two, as a running example. 
Markus Sch\"oberl, Andreas Siuka
math.OC math.AP math.DG math.DS