Geometric angle for rotated rotators, and the Hannay angle of the world

A simple formula is derived for the shift in angle variable (Hannay angle) arising from a slow (adiabatic) cycle of a parameter in a one-dimensional classical system. The formula is illustrated by numerical computations for different degrees of smoothness of the adiabatic driving. If the driving is smooth enough, the adiabatic invariant is sufficiently well conserved to enable fluctuations in the frequency to be neglected when computing the dynamical angle contribution to the final angle. If not (e.g. if the driving is uniform over a finite time), these fluctuations must be taken into account. The Hannay angle appears as a small change in period of a celestial body (Earth) rotating about another body (Sun) caused by the slow revolution of a third body (Jupiter).