Interplay between Airy and Coriolis precessions in a real Foucault pendulum

Abstract

We study the precession of a Foucault pendulum using a new approach. We characterize the support anisotropy by the difference between the maximum and minimum periods of the pendulum along the principal axes of the support. Then we compute the total precession rate, taking into account both the Airy precession of a spherical pendulum and the Coriolis precession due to the Earth's rotation. To study the resulting motion we developed a calculation loop, period after period, which describes the movement of the oscillatory trajectory of the bob. To test our model, we mounted a test pendulum of 480.3 cm length and measured its periods and precession. The rate of precession is sensitive to the dimensions of the pendulum, the anisotropy of the support, and the initial conditions. We find that for certain amplitudes the precession can stop entirely, while the pendulum continues to oscillate. It is also possible to obtain continuous precession at lower oscillation amplitudes. We give an upper bound for this critical oscillation amplitude. We close with a discussion of the implications of our findings for the design of Foucault pendulums used in demonstrations and lab experiments.