Incomplete Dirac reduction of constrained Hamiltonian systems
Chaotic Dynamics
2014-12-17 v1
Abstract
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac-Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed.
Keywords
Cite
@article{arxiv.1412.4922,
title = {Incomplete Dirac reduction of constrained Hamiltonian systems},
author = {C. Chandre},
journal= {arXiv preprint arXiv:1412.4922},
year = {2014}
}