  The presence of symmetries in a Hamiltonian system usually implies the
existence of conservation laws that are represented mathematically in terms of
the dynamical preservation of the level sets of a momentum mapping. The
symplectic or Marsden--Weinstein reduction procedure takes advantage of this
and associates to the original system a new Hamiltonian system with fewer
degrees of freedom. However, in a large number of situations, this standard
approach does not work or is not efficient enough, in the sense that it does
not use all the information encoded in the symmetry of the system. In this
work, a new momentum map will be defined that is capable of overcoming most of
the problems encountered in the traditional approach.
