Regular Article

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

Université du Québec à Chicoutimi, 555 Boulevard de l'Université, Saguenay, QC G7H 2B1, Canada

^a e-mail: rverreau@uqac.ca

Received: 2 September 2016
Revised: 30 June 2017
Accepted: 30 June 2017
Published online: 4 August 2017

Abstract

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes’ dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2–3 orders of magnitude is achieved.