2012/10/03 by Ünver Çiftçi, Çiftçi, Ünver
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #53C15 #53D17 #70H99 #Control and Stability of Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Microtubule and mitosis dynamics #math-ph #math.DG #math.MP #msc:53C15 #msc:53D17 #msc:70H99
paper · pdf · doi:10.48550/arxiv.1210.1042
Submitted to JGM
openalex publication_date 2012/10/03 · arxiv created 2013/03/04 · arxiv updated 2013/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.