The Foucault pendulum as an example of motion on a pseudo-surface

Abstract

The Foucault pendulum is shown to be an example of motion on a pseudo-surface, and the consequences of that are explored. In particular, its first and second fundamental forms are obtained, as well as its Gaussian and mean curvatures and the equations of its geodesics. However, a physical consideration that relates to the extension from space to space-time introduces a complication into the discussion of the geometry of the Foucault pseudo-surface that relates to the possible signatures of the space-time metric.