A trajectory equation for walking droplets : hydrodynamic pilot-wave theory

@inproceedings{Oza2013ATE,
title={A trajectory equation for walking droplets : hydrodynamic pilot-wave theory},
author={Anand U. Oza and R. R. Rosales and John W. M. Bush},
year={2013}
}

We present the results of a theoretical investigation of droplets bouncing on a vertically vibrating fluid bath. An integro-differential equation describing the horizontal motion of the drop is developed by approximating the drop as a continuous moving source of standing waves. Our model indicates that, as the forcing acceleration is increased, the bouncing state destabilizes into steady horizontal motion along a straight line, a walking state, via a supercritical pitchfork bifurcation… CONTINUE READING