Singularities of the hamiltonian vectorfield in nonautonomous variational
problems
Abstract
Variational problems with n degrees of freedom give rise (by Pontriaguine
ma-ximum principle) to a hamiltonian vectorfield in T*Rn , that
presents singularities (non smoothness points) when the lagrangean is not convex.
For one degree of freedom nonautonomous problems of the calculus of varia-tions
where the hamiltonian vectorfield in T*R depends explicitly on
the time, we consider the associated autonomous vectorfield in
T*Rx Rand classify its sin-gularites up to an equivalence that
takes into account the special rö ole played by the time coordinate, i. e. that
respects the foliation of T*Rx R into planes of constant time.