Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures

Details Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures

2010-10-13

arxiv.org/abs/1010.2547v1

Mathematics

Differential Geometry

6 pages

Scientific paper

We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, we recover not only the standard structure matrix of Stokes-Dirac structures, but also the typical non-canonical advection terms in (for instance) the Euler equation.

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