Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures
Differential Geometry
2010-10-14 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1010.2547,
title = {Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures},
author = {Joris Vankerschaver and Hiroaki Yoshimura and Melvin Leok and Jerrold E. Marsden},
journal= {arXiv preprint arXiv:1010.2547},
year = {2010}
}
Comments
6 pages