Leibniz - Dirac Structures and Nonconservative Systems with Constraints
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Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Amer Inst Mathematical Sciences-Aims
Access Rights
info:eu-repo/semantics/openAccess
Abstract
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 such as gradient and metriplectic systems with constraints. We define Leibniz-Dirac structures which lead to a natural generalization of Dirac and Riemannian structures, for instance. From modeling point of view, Leibniz-Dirac structures make it easy to formulate implicit dissipative Hamiltonian systems. We give their exact characterization in terms of bundle maps from the tangent bundle to the cotangent bundle and vice verse. Physical systems which can be formulated in terms of Leibniz-Dirac structures are discussed.
Description
Keywords
Dirac manifolds, dissipative Hamiltonian systems, gradient systems, Hamiltonian-Systems, Algebroids, Equations
Journal or Series
Journal of Geometric Mechanics
WoS Q Value
Q2
Scopus Q Value
Volume
5
Issue
2
