We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in  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.
|Number of pages||17|
|Journal||Mathematical and Computer Modelling of Dynamical Systems|
|Publication status||Published - Dec 2002|
- linear Hamiltonian systems
- linear variational systems
- multi-variable polynomial matrices
- bilinear- and quadratic differential forms