2012/08/09 by Hernán Cendra, Cendra, Hernán, María Etchechoury +3
Engineering · Mathematics · Physics and Astronomy · #70H45 (Primary) 70G45 (Secondary) #Algebra over a field #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Dirac (video compression format) #Dirac algebra #Dirac equation #Dynamical systems theory #Engineering #FOS: Physical sciences #Foliation (geology) #Geometry #Hamiltonian system #Integrable system #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Theoretical physics #Theory of constraints #math-ph #math.MP #msc:70G45 #msc:70H45
paper · pdf · doi:10.48550/arxiv.1208.1953
published in arXiv (Cornell University) (Cornell University) · Article withdrawn and moved to arXiv:1106.3354v2 (no changes made, arXiv entries merged)
openalex publication_date 2012/08/09 · arxiv created 2012/11/14 · arxiv updated 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends the Gotay-Nester and the Dirac theories of constrained\nsystems in order to deal with Dirac dynamical systems in the integrable case.\nIntegrable Dirac dynamical systems are viewed as constrained systems where the\nconstraint submanifolds are foliated, the case considered in Gotay-Nester\ntheory being the particular case where the foliation has only one leaf. A\nConstraint Algorithm for Dirac dynamical systems (CAD), which extends the\nGotay-Nester algorithm, is developed. Evolution equations are written using a\nDirac bracket adapted to the foliations and an abridged total energy which\ncoincides with the total Hamiltonian in the particular case considered by\nDirac. The interesting example of LC circuits is developed in detail. The paper\nemphasizes the point of view that Dirac and Gotay-Nester theories are dual and\nthat using a combination of results from both theories may have advantages in\ndealing with a given example, rather than using systematically one or the\nother.\n