Kurt Schlacher, Markus Schöberl,
"How to Choose the State for Distributed-Parameter Systems, a Geometric Point of View"
: Proceedings, 8th Vienna International Conference on Mathematical Modelling, 2015
How to Choose the State for Distributed-Parameter Systems, a Geometric Point of View
Sprache des Titels:
Proceedings, 8th Vienna International Conference on Mathematical Modelling
The choice of the state for a distributed-parameter system has some subtleties. The group of structure preserving maps or bundle morphisms, which map states to states and state and inputs to inputs is often rich enough for explicit control systems described by ODEs. In contrast the group of admissible maps is not limited to morphisms in the PDE case. The best known example is the wave equation, where two different descriptions
in electrical and mechanical engineering are used, which are not linked by a bundle morphism. This contribution is limited to Hamiltonian and Lagrangian systems, where it is shown, how different descriptions can be derived from the same variational principle by standard and non standard transformations. In particular, we consider beams and plates.