Second-order Lagrangians admitting a second-order Hamilton-Cartan formalism

The Poincare-Cartan (PC) form of a Lagrangian on the bundle J(2) = J(2) (N, M) is, as a general rule, defined on J(3) thus leading to a non-equivalenc e between Euler-Lagrange and Hamilton-Cartan equations. This naturally lead s to the problem of determining what Lagrangians have a PC form projectable onto J(2), as they will then admit a second-order Hamiltonian formalism. T here are specific examples of this phenomenon in field theory. This paper p rovides an explicit classification of such Lagrangians.