Hamiltonian and Variational Linear Distributed Systems

Linear Hamiltonian systems

We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external influences, and allows to study systems described by higher-order differential equations, thus dispensing with the usual point of view in c...

Linear openness and variational systems

In this paper we investigate under which conditions the composition of two set-valued maps enjoys the linear openness property. To obtain our results, we use the Nadler’s fixed point theorem, and Lim’s lemma which provides an estimate for the distance between the sets of fixed points of two (set-valued) contractions. As an application, we obtain the Lipschitz property of the implicit solution m...

Distributed-Parameter Port-Hamiltonian Systems

Oscillation of Linear Hamiltonian Systems

We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.

Variational Discrete Dirac Mechanics—implicit Discrete Lagrangian and Hamiltonian Systems

We construct discrete analogues of Tulczyjew’s triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian and Hamiltonian systems, while incorporating discrete Dirac constraints. In particular, this yields implicit nonholonomic Lagrangia...