  We introduce a solvable Lagrangian model for droplet bouncing. The model
predicts that, for an axisymmetric drop, the contact time decreases to a
constant value with increasing Weber number, in qualitative agreement with
experiments, because the system is well approximated as a simple harmonic
oscillator. We introduce asymmetries in the velocity, initial droplet shape,
and contact line drag acting on the droplet and show that asymmetry can often
lead to a reduced contact time and lift-off in an elongated shape. The model
allows us to explain the mechanisms behind non-axisymmetric bouncing in terms
of surface tension forces. Once the drop has an elliptical footprint the
surface tension force acting on the longer sides is greater. Therefore the
shorter axis retracts faster and, due to the incompressibility constraints,
pumps fluid along the more extended droplet axis. This leads to a positive
feedback, allowing the drop to jump in an elongated configuration, and more
quickly.
