Oza, A. U., Harris, D. M., Rosales, R. R., & Bush, J. W. (2014). Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. *Journal of Fluid Mechanics*, *744*, 404-429.

We present the results of a theoretical investigation of droplets walking on a

rotating vibrating ﬂuid bath. The droplet’s trajectory is described in terms of an

integro-differential equation that incorporates the inﬂuence of its propulsive wave

force. Predictions for the dependence of the orbital radius on the bath’s rotation

rate compare favourably with experimental data and capture the progression from

continuous to quantized orbits as the vibrational acceleration is increased. The orbital

quantization is rationalized by assessing the stability of the orbital solutions, and may

be understood as resulting directly from the dynamic constraint imposed on the drop

by its monochromatic guiding wave. The stability analysis also predicts the existence

of wobbling orbital states reported in recent experiments, and the absence of stable

orbits in the limit of large vibrational forcing