  Time-averaged trapping potentials have played an important role in the
development of the field of ultracold atoms. Despite their widespread
application, there is not yet a complete understanding of when a system can be
considered time-averaged. Here we use Floquet theory to analyse the lowest
energy state of time-periodic trapping potentials, and characterise the
transition from a localised state in a slowly moving trap to a delocalised
state in a rapidly oscillating time-averaged potential. We investigate how the
driving parameters affect the density and phase of the Floquet ground state,
and provide a quantitative measure of the degree to which they can be
considered time-averaged. We study a number of simple representative systems,
and comment on the features affecting the experimental realisation of
time-averaged trapping potentials.
