On Stokes-Lagrange and Stokes-Dirac representations for 1D distributed port-Hamiltonian systems

Port-Hamiltonian systems were recently extended to include implicitly defined energy and energy ports thanks to a (Stokes-)Lagrange subspace. Here, we study the equivalent port-Hamiltonian representations of two systems with damping, written using either a classical Hamiltonian or a Stokes-Lagrange subspace. Then, we study the Timoshenko beam and Euler-Bernoulli models, the latter being the flow-constrained version of the former, and show how they can be written using either a Stokes-Dirac or Stokes-Lagrange subspace related by a transformation operator. Finally, it is proven that these transformations commute with the flow-constraint projection operator.

To cite this paper:
Bendimerad-Hohl Antoine, Matignon Denis, Haine Ghislain, Lefèvre Laurent (2024) On Stokes-Lagrange and Stokes-Dirac representations for 1D distributed port-Hamiltonian systems. IFAC-PapersOnLine 58(17):238–243. Cambridge, United Kingdom.

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