Degenerate time-dependent Lagrangians of second order: 
the fourth order differential equation problem

Manuel de Le\'on \and Juan C. Marrero

Abstract. We develop a constraint algorithm for degenerate
time-dependent Lagrangians of second order and solve the
so-called fourth order differential equation problem. The study
is inspired in the Gotay and Nester constraint algorithm and the
notion of intermediate spaces introduced by Gr\`acia, Pons and
Rom\'an-Roy.

Keywords. Degenerate, time-dependent, higher order Lagrangians,
constraint algorithm.

MS classification. 58F05, 53C15, 53C05, 70H35.