  In this paper we consider an alternative approach to "un-reduction". This is
the process where one associates to a Lagrangian system on a manifold a
dynamical system on a principal bundle over that manifold, in such a way that
solutions project. We show that, when written in terms of second-order ordinary
differential equations (SODEs), one may associate to the first system a (what
we have called) "primary un-reduced SODE", and we explain how all other
un-reduced SODEs relate to it. We give examples that show that the considered
procedure exceeds the realm of Lagrangian systems and that relate our results
to those in the literature.
