Reduction of Hamilton-Dirac Equation in Presymplectic Dynamics

ABSTRACT: In a geometric formulation [3] of Dirac’s generalized Hamiltonian dynamics [6], Hamilton-Dirac equation is the name given to a kind of differential equation (in implicit form) on a presymplectic manifold, which naturally generalizes the notion of locally or globally Hamiltonian equation (in normal form) on a symplectic manifold. A general geometric framework already developped for implicit differential equations [4], is here applied to Hamilton-Dirac equation with the aim of investigating its reducibility to Hamiltonian form on some (lower-dimensional) quotient manifold and its subsequent reconstruction. The classical reduction-reconstruction problems of symplectic dynamics, will neatly be framed into the above theoretical context.