  The equations for the equilibrium of a thin elastic ribbon are derived by
adapting the classical theory of thin elastic rods. Previously established
ribbon models are extended to handle geodesic curvature, natural out-of-plane
curvature, and a variable width. Both the case of a finite width (Wunderlich's
model) and the limit of small width (Sadowksky's model) are recovered. The
ribbon is assumed to remain developable as it deforms, and the direction of the
generatrices is used as an internal variable. Internal constraints expressing
inextensibility are identified. The equilibrium of the ribbon is found to be
governed by an equation of equilibrium for the internal variable involving its
second-gradient, by the classical Kirchhoff equations for thin rods, and by
specific, thin-rod-like constitutive laws; this extends the results of
Starostin and van der Heijden (2007) to a general ribbon model. Our equations
are applicable in particular to ribbons having geodesic curvature, such as an
annulus cut out in a piece of paper. Other examples of application are
discussed. By making use of a material frame rather than the Fr\'enet-Serret's
frame, the present work unifies the description of thin ribbons and thin rods.
