Modified Hamiltonian formalism for higher-derivative theories

An alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach, it has the following advantages: (i) The Lagrangian, when expressed in terms of new variables, yields proper equations of motion; no additional Lagrange multipliers are necessary. (ii) The Legendre transformation can be performed in a straightforward way, provided the Lagrangian is nonsingular in the Ostrogradski sense. The generalizations to singular Lagrangians as well as field theory are presented.