  We consider a class of Lagrangians that depend not only on some
configurational variables and their first time derivatives, but also on second
time derivatives, thereby leading to fourth-order evolution equations. The
proposed higher-order Lagrangians are obtained by expressing the variables of
standard Lagrangians in terms of more basic variables and their time
derivatives. The Hamiltonian formulation of the proposed class of models is
obtained by means of the Ostrogradsky formalism. The structure of the
Hamiltonians for this particular class of models is such that constraints can
be introduced in a natural way, thus eliminating expected instabilities of the
fourth-order evolution equations. Moreover, canonical quantization of the
constrained equations can be achieved by means of Dirac's approach to
generalized Hamiltonian dynamics.
