An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems

Autor: Hernán Cendra, María del Rosario Etchechoury, Sebastián J. Ferraro
Rok vydání: 2012
Předmět:
Control and Optimization
Dynamical systems theory
Integrable system
Matemáticas
Dirac (software)
FOS: Physical sciences
Matemática Pura
purl.org/becyt/ford/1 [https]
IMPLICIT DIFFERENTIAL EQUATIONS
Constrained systems
symbols.namesake
Theoretical physics
Constraint algorithm
Dirac structures
70H45 (Primary) 70G45 (Secondary)
Point (geometry)
NONHOLONOMIC MECHANICS
Implicit differential equations
Mathematical Physics
Mathematics
Ingeniería Mecánica
Applied Mathematics
DIRAC STRUCTURES
purl.org/becyt/ford/1.1 [https]
Mathematical Physics (math-ph)
Poisson geometry
Constraint (information theory)
POISSON GEOMETRY
70H45 (Primary)
70G45 (Secondary)
Mechanics of Materials
Nonholonomic mechanics
symbols
Foliation (geology)
CONSTRAINED SYSTEMS
Geometry and Topology
CIENCIAS NATURALES Y EXACTAS
Dirac bracket
Zdroj: SEDICI (UNLP)
Universidad Nacional de La Plata
instacron:UNLP
CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
DOI: 10.48550/arxiv.1208.1953
Popis: This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated, the case considered in Gotay-Nester theory being the particular case where the foliation has only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an abridged total energy which coincides with the total Hamiltonian in the particular case considered by Dirac. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.
Comment: 78 pages; moved here from the old entry arXiv:1208.1953; v1 contains more detailed explanations of some issues
Databáze: OpenAIRE
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