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

TL;DR

This paper models the Foucault pendulum's motion as a pseudo-surface, deriving its geometric properties and exploring implications of space-time considerations on its geometry.

Contribution

It introduces a novel geometric framework for analyzing the Foucault pendulum as a pseudo-surface, including fundamental forms and geodesic equations.

Findings

Derived the first and second fundamental forms of the pseudo-surface

Calculated Gaussian and mean curvatures of the Foucault pseudo-surface

Discussed the impact of space-time signatures on the geometry

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.