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Hamiltonian and Variational Linear Distributed Systems

Hamiltonian and Variational Linear Distributed Systems
Hamiltonian and Variational Linear Distributed Systems
We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary linear constant-coefficient differential equations is Hamiltonian if and only if it is variational. In this paper we extend this result to systems described by linear, constant-coefficient partial differential equations. It is shown that any variational system is Hamiltonian, and that any scalar Hamiltonian system is contained (in general, properly) in a particular variational system.
Linear Hamiltonian systems, linear variational systems, multi-variable polynomial matrices, bilinear- and quadratic differential forms.
457-473
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450

Rapisarda, Paolo and Trentelman, Harry L. (2002) Hamiltonian and Variational Linear Distributed Systems. Mathematical and Computer Modeling of Dynamical Systems, 8 (4), 457-473.

Record type: Article

Abstract

We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary linear constant-coefficient differential equations is Hamiltonian if and only if it is variational. In this paper we extend this result to systems described by linear, constant-coefficient partial differential equations. It is shown that any variational system is Hamiltonian, and that any scalar Hamiltonian system is contained (in general, properly) in a particular variational system.

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Published date: December 2002
Keywords: Linear Hamiltonian systems, linear variational systems, multi-variable polynomial matrices, bilinear- and quadratic differential forms.
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 262215
URI: http://eprints.soton.ac.uk/id/eprint/262215
PURE UUID: f187feb5-5c4f-4670-8718-75d696fe9366

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Date deposited: 30 Mar 2006
Last modified: 14 Mar 2024 07:06

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Contributors

Author: Paolo Rapisarda
Author: Harry L. Trentelman

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