  This paper aims to provide a new problem formulation of path following for
mechanical systems without time parameterization nor guidance laws, namely, we
express the control objective as an orbital stabilization problem. It is shown
that, it is possible to adapt the immersion and invariance technique to design
static state-feedback controllers that solve the problem. In particular, we
select the target dynamics adopting the recently introduced Mexican sombrero
energy assignment method. To demonstrate the effectiveness of the proposed
method we apply it to control underactuated marine surface vessels.
