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This paper extends the Gotay-Nester and the Dirac theories of constrainedsystems in order to deal with Dirac dynamical systems in the integrable case.Integrable Dirac dynamical systems are viewed as constrained systems where theconstraint submanifolds are foliated, the case considered in Gotay-Nestertheory being the particular case where the foliation has only one leaf. AConstraint Algorithm for Dirac dynamical systems (CAD), which extends theGotay-Nester algorithm, is developed. Evolution equations are written using aDirac bracket adapted to the foliations and an abridged total energy whichcoincides with the total Hamiltonian in the particular case considered byDirac. The interesting example of LC circuits is developed in detail. The paperemphasizes the point of view that Dirac and Gotay-Nester theories are dual andthat using a combination of results from both theories may have advantages indealing with a given example, rather than using systematically one or theother.

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