  We present a study of the macroscopic dynamics of a polariton condensate
formed by non-resonant optical excitation in a quasi-one-dimensional
ring-shaped microcavity. The presence of a gradient in the cavity photon energy
creates a macroscopic trap for the polaritons in which a single mode condensate
is formed. With time- and energy-resolved imaging we show the role of
interactions in the motion of the condensate as it undergoes equilibration in
the ring. These experiments also give a direct measurement of the
polariton-polariton interaction strength above the condensation threshold. Our
observations are compared to the open-dissipative one-dimensional
Gross-Pitaevskii equation which shows excellent qualitative agreement.
