Local existence of Dynamically Allowed Brackets and a local existence of a Hamiltonian associated with these Brackets, for a given, possibly time dependent, N-dimensional Equations of Motion that may include Constraints

Dynamically Allowed Brackets are defined for given equations of motion for an N-dimensional mechanical system. The equations of motion may be explicitly time dependent, and may include explicitly time dependent constraints. Local existence of the Dynamically Allowed Brackets is shown. The local existence of a Hamiltonian reproducing the given equations of motion with the use of these Dynamically Allowed Brackets is proven.