How to Choose the State for Distributed-Parameter Systems, a Geometric Point of View
Sprache des Vortragstitels:
8th Vienna International Conference on Mathematical Modelling
Sprache des Tagungstitel:
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.