  (Abridged) A simple and general description of the dynamics of a narrow
eccentric ring is presented.We view an eccentric ring which precesses uniformly
at a slow rate as exhibiting a global $m=1$ mode originating from a standing
wave superposed on an axisymmetric background.We adopt a continuum description
using the language of fluid dynamics which gives equivalent results for the
secular dynamics of thin rings as the the well known description using discrete
elliptical streamlines formulated by Goldreich and Tremaine (1979). We use this
to discuss the non linear mode interactions that appear through the excitation
of higher $m$ modes due to the coupling of the $m=1$ mode with an external
satellite potential, showing that they can lead to the excitation of the $m=1$
mode through a feedback process.Two conditions for the maintainance of a steady
$m=1$ mode are obtained. One,being the condition for the normal mode pattern to
precess uniformly requires a balance between the differential precession
induced by the oblateness of the central planet,self-gravity and collisional
effects and is the continuum form of that obtained from the $N$ streamline
model of Goldreich and Tremaine (1979).The other condition is for the steady
maintenance of the non-zero radial action of the ring on account of the normal
mode.This requires a balance between input due to eccentric resonances due to
external satellites and additional collisional damping associated with the
presence of the $m=1$ mode We estimate that such a balance can occur in the
$\epsilon-$ring of Uranus,given its currently observed physical and orbital
parameters.
