Dirac geometric structures

T. V. Salnikova, E. I. Kugushev

Lomonosov Moscow State University, Moscow, Russia

Abstract: For Hamiltonian systems on symplectic manifolds with constraints in the Dirac model of generalized Hamiltonian dynamics, V. V. Kozlov considered the operation of symplectic projection of a Hamiltonian vector field for the case of generalized nonintegrable differential constraints. This paper considers a constraint regularization method that circumvents the degeneracy of the symplectic projection operation in the case of an odd number of constraints. The method is based on embedding of the original system into an extended system of higher dimension with an increased number of constraints.

Keywords: Hamilton's equations, differential constraints, symplectic projection.

UDC: 514.8

DOI: 10.22363/2413-3639-2025-71-4-655-662