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Dirac brackets in constrained dynamics

delete1999-06-01
delete39
PRE
AI
A
Alberto Ibort
M
Manuel de León
J
Juan Carlos Marrero
D
de Diego, DM
DOI：10.1002/(SICI)1521-3978(199906)47:5<459::AID-PROP459>3.0.CO;2-Edelete
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Abstract

Abstract

En 中文
An unified geometric description of various Dirac brackets for regular and singular lagrangians with holonomic or non-holonomic constraints is presented. Such unified picture relies only on two simple physical arguments: classical complementarity principle and principle of deterministic evolution. The appropriate geometrization of these principles allows to construct a recursive constraint algorithm that eventually produces a maximal final state manifold where a well defined dynamics exists, naturally equipped with a Dirac bracket such that the dynamics is hamiltonian with respect to it. A classification of constraints in first and second class as envisaged by Dirac emerges also naturally from this picture. The Dirac brackets constructed show explicitly the existence of classical anomalies for such lagrangian theories since in general they do not verify Jacobi's identity. Such features are discussed using a variety of examples.
Keywords:
NONHOLONOMIC LAGRANGIAN SYSTEMS
GEOMETRICAL FRAMEWORK
MECHANICAL SYSTEMS
ALGORITHM
PROJECTOR
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Journal

F
Fortschritte der Physik-Progress of Physics
IF:
7.8
Papers:
2.0K
Citations:
3.6K

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