# Canonical Interdomain Coupling in Distributed Parameter Systems: An Extension of the Symplectic Gyrator

Canonical Interdomain Coupling in Distributed Parameter Systems: An Extension of the Symplectic... <jats:title>Abstract</jats:title> <jats:p>In this paper we propose a bond graph formulation of interdomain coupling extending the symplectic gyrator proposed in the so-called generalized or thermodynamic bond graph formalism. Therefore we use as power and energy variables exterior differentiable k-forms on the Euclidean space. The bonds and power variables are of two types: the first type represents the energy flows inside a domain Ω of the Euclidean space and the second type represent the energy flows through the boundary ∂Ω of the domain. It will be shown that the interdomain coupling may be represented as a 3-port power continuous element, called Stokes-Dirac Junction Structure, whose constitutive relation is defined using solely the exterior derivative of k-forms. This general result is applied to the examples of a transmission line, the electro-magnetic field and the vibrating string.</jats:p> http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dynamic Systems and Control CrossRef

# Canonical Interdomain Coupling in Distributed Parameter Systems: An Extension of the Symplectic Gyrator

Dynamic Systems and ControlNov 11, 2001

## Canonical Interdomain Coupling in Distributed Parameter Systems: An Extension of the Symplectic Gyrator

### Abstract

<jats:title>Abstract</jats:title>
<jats:p>In this paper we propose a bond graph formulation of interdomain coupling extending the symplectic gyrator proposed in the so-called generalized or thermodynamic bond graph formalism. Therefore we use as power and energy variables exterior differentiable k-forms on the Euclidean space. The bonds and power variables are of two types: the first type represents the energy flows inside a domain Ω of the Euclidean space and the second type represent the energy flows through the boundary ∂Ω of the domain. It will be shown that the interdomain coupling may be represented as a 3-port power continuous element, called Stokes-Dirac Junction Structure, whose constitutive relation is defined using solely the exterior derivative of k-forms. This general result is applied to the examples of a transmission line, the electro-magnetic field and the vibrating string.</jats:p>

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Publisher
CrossRef
DOI
10.1115/imece2001/dsc-24546
Publisher site
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### Abstract

<jats:title>Abstract</jats:title> <jats:p>In this paper we propose a bond graph formulation of interdomain coupling extending the symplectic gyrator proposed in the so-called generalized or thermodynamic bond graph formalism. Therefore we use as power and energy variables exterior differentiable k-forms on the Euclidean space. The bonds and power variables are of two types: the first type represents the energy flows inside a domain Ω of the Euclidean space and the second type represent the energy flows through the boundary ∂Ω of the domain. It will be shown that the interdomain coupling may be represented as a 3-port power continuous element, called Stokes-Dirac Junction Structure, whose constitutive relation is defined using solely the exterior derivative of k-forms. This general result is applied to the examples of a transmission line, the electro-magnetic field and the vibrating string.</jats:p>

### Journal

Dynamic Systems and ControlCrossRef

Published: Nov 11, 2001

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