Hamiltonian formulation of distributed-parameter systems with boundary energy flow
Authors
A.J. van der Schaft, B.M. Maschke
Abstract
A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes’ theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell’s equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore, the framework is extended to cover Euler’s equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes–Dirac structure are investigated, including the analysis of conservation laws.
Keywords
Distributed-parameter systems; Hamiltonian systems; Boundary variables; Dirac structures; Stokes’ theorem; Conservation laws
Citation
- Journal: Journal of Geometry and Physics
- Year: 2002
- Volume: 42
- Issue: 1-2
- Pages: 166–194
- Publisher: Elsevier BV
- DOI: 10.1016/s0393-0440(01)00083-3
BibTeX
@article{van_der_Schaft_2002,
title={{Hamiltonian formulation of distributed-parameter systems with boundary energy flow}},
volume={42},
ISSN={0393-0440},
DOI={10.1016/s0393-0440(01)00083-3},
number={1–2},
journal={Journal of Geometry and Physics},
publisher={Elsevier BV},
author={van der Schaft, A.J. and Maschke, B.M.},
year={2002},
pages={166--194}
}
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