Presymplectic form

In geometric mechanics a presymplectic form is a closed differential 2-form of constant rank on a manifold.^[1] However, some authors use different definitions. Recently, Hajduk and Walczak defined a presymplectic form as a closed differential 2-form of maximal rank on a manifold of odd dimension.^[2] A symplectic form is a presymplectic form that is also nondegenerate.^[3] Lack of nondegeneracy, leading to presymplectic forms, occurs in dynamical systems with singular Lagrangians, Hamiltonian systems with constraints and control theory.^[4]