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.