Momentum section on Courant algebroid and constrained Hamiltonian mechanics

We propose a generalization of the momentum map on symplectic manifold with Lie algebra action to Courant algebroid structure. The theory section is generalized compatible algebroid. As an example, we identify in constrained Hamiltonian mechanics symmetry. Moreover, construct cohomological formulations by considering BFV and BV formalism this system. Weil for structure constructed.