On the relation between energy conserving low-order models and Hamiltonian systems

In this paper we examine the relation between the energy conserving finite dimensional or low-order models obtained by the application of the Galerkin projection methods to infinite dimensional model, and the class of finite dimensional non-canonical Hamiltonian systems with quadratic Hamiltonian functions and structure matrix whose elements are linear function of the state. We also examine the conditions for the conservation of the phase volume. (C) 2008 Elsevier Ltd. All rights reserved.