Leibniz-Dirac structures and nonconservative systems with constraints

Ünver Çiftçi

doi:10.3934/jgm.2013.5.167

Article Contents

2013, Volume 5, Issue 2: 167-183. Doi: 10.3934/jgm.2013.5.167

This issue Previous Article Canonoid transformations and master symmetries Next Article The supergeometry of Loday algebroids

Leibniz-Dirac structures and nonconservative systems with constraints

Ünver Çiftçi^1,

1.
Department of Mathematics, Namik Kemal University, 59030 Tekirdaǧ

Received: September 2012

Revised: April 2013

Published: June 2013

Abstract / Introduction Related Papers Cited by

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 vector 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.

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Mathematics Subject Classification: 53D05, 70F25, 70G45.

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