  We present the results of a theoretical investigation of the dynamics of a
droplet walking on a vibrating fluid bath under the influence of a harmonic
potential. The walking droplet's horizontal motion is described by an
integro-differential trajectory equation, which is found to admit steady
orbital solutions. Predictions for the dependence of the orbital radius and
frequency on the strength of the radial harmonic force field agree favorably
with experimental data. The orbital quantization is rationalized through an
analysis of the orbital solutions. The predicted dependence of the orbital
stability on system parameters is compared with experimental data and the
limitations of the model are discussed.

Fluid Dynamics