Anisosphere analysis of the equivalence between a precessing Foucault pendulum and a torsional balance

Abstract

The residual anisotropy of a real Foucault pendulum is responsible for an oscillatory behaviour of the precession angle according to the original description given by Kamerlingh Onnes in his dissertation. A simulation of the experimental procedure of enchained runs, consisting of starting a short experiment at the azimuth at which a precedent similar experiment has been stopped, has been performed using the anisosphere model. It leads to the conclusion that the precessing pendulum undergoes oscillations in precession associated with an extremely shallow potential well analogous to the potential well of a very slow torsional balance. Such systems are therefore rendered sensitive to extremely-low-energy perturbations. To the author’s knowledge, the hypersensitivity of the oscillatory precession of the anisotropic Foucault pendulum has been unravelled for the first time thanks to the analysis and visualization power of the anisosphere model. In particular, the periodic apparent motion of celestial bodies appears to modify the anisotropy characteristic of the precession potential well. This may provide likelihood for the similar responses of the paraconical pendulum of Allais during the 1950’s and of the torsion pendulum of Saxl and Allen in 1970 to certain Sun-Moon-Earth syzygies.