1210.1042 (Ünver Çiftçi)

Leibniz-Dirac structures and dissipative Hamiltonian systems with
constraints    [PDF]

Ünver Çiftçi

Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems and gradient systems with constraints. We define Leibniz-Dirac (LD) structures which lead to a natural generalization of Dirac and Riemannian structures, for instance. From modeling point of view, LD structures make it easy to formulate implicit dissipative Hamiltonian systems. We give their exact characterization in terms of bundle maps from the cotangent bundle into the tangent bundle. Their behavior under push-forward maps is also considered. Physical systems which can be formulated in terms of LD structures are discussed.

View original: http://arxiv.org/abs/1210.1042