  This work propose an alternative and systematic way to obtain a canonical
Lagrangian formulation for rotational systems. This will be done in the
symplectic framework and with the introduction of extra variables which enlarge
the phase space. In fact, this formalism provides a remarkable and new result
to compute the canonical Lagrangian formulation for rotational systems, {\it
i.e.}, the obstruction to the construction of a canonical formalism can be
solved in an arbitrary way and, consequently, a set of dynamically equivalent
Lagrangian descriptions can be computed.
