Markus Schöberl, Kurt Schlacher,
"On the extraction of the boundary conditions and the boundary ports in second-order field theories"
, in Journal of Mathematical Physics, 10-2018
On the extraction of the boundary conditions and the boundary ports in second-order field theories
Sprache des Titels:
In this paper we consider second-order field theories in a variational setting. From the
variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well
known that this is not true for the Cartan form. This has also consequences on the derivation
of the boundary conditions when non trivial variations are allowed on the boundary. By posing
extra conditions on the set of possible boundary terms we exploit the degree of freedom in
the Cartan form to extract physical meaningful boundary expressions. The same mathematical
machinery will be applied to derive the boundary ports in a Hamiltonian representation of the
partial differential equations which is crucial for energy based control approaches. Our results
will be visualized for mechanical systems such as beam and plate models.