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

Hamiltonian formulation of a class of constrained fourth-order differential equations in the Ostrogradsky framework