On the inverse problem in the Hamiltonian formalism for a system of
second-order ODEs
Abstract
Two procedures for finding a Hamiltonian for a system of n
second-order ODEs, without determining any of its first integrals, are
provided. The first procedure is based on the existence of a regular
Lagrangian, while the second is based on the existence of a closed
invariant two-form of maximal rank. Examples are given to illustrate
these procedures.