Stabilisation of the swing pattern of an anisotropic simple pendulum

Abstract

The suppression of the effects of anisotropy on a pendulum by use of a rotating mount was initially envisaged by Léon Foucault, based on his observations of the vibrations of a rod clamped in a lathe. However, the method seems to never have been tried due to the practical difficulties involved. We report a computational study of the stabilisation of the swing pattern of a simple pendulum, showing anisotropic behaviour in a static configuration, by rotation of the system mount. When the mount is static, for most initial conditions the swing patterns quickly evolves into unstable, complex Lissajous-like patterns. When the pendulum mount is rotated faster than the pendulum frequency effects of anisotropy are suppressed, and the swing pattern stabilises to that of an isotropic 3D simple pendulum. Suppression of mount anisotropy influence occurs for relatively low rotation rates. We also study swing evolution in the presence of random variations in the orientation of the mount principal axes. The use of computational techniques confirms Foucault’s original observations and hypothesis and provides an interesting avenue for students to engage meaningfully with this historically important and inspiring experiment in a novel and challenging manner.