Hamiltonian and Variational Linear Distributed Systems

P. Rapisarda and H.L. Trentelman

Mathematical and Computer Modelling of Dynamical Systems, 2002, vol. 8, issue 4, 457-473

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.

Date: 2002
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DOI: 10.1076/mcmd.8.4.457.15850

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