English

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

R2 v1 2026-06-21T16:27:39.676Z