Non inertial dynamics and holonomy on the ellipsoid

TL;DR

This paper explores the classical effects of inertial forces and their geometric interpretation through holonomy on an ellipsoid, challenging common assumptions about Foucault pendulum precession.

Contribution

It provides a detailed analysis of inertial forces in Newtonian mechanics and examines the relationship between Foucault pendulum precession and holonomy on an ellipsoid.

Findings

Inertial forces can be understood geometrically on an ellipsoid.

The precession of the Foucault pendulum is not always equivalent to holonomy on the sphere.

Critical remarks on the common statement relating pendulum precession to holonomy.

Abstract

Traditionally, the discussion about the geometrical interpretation of inertial forces is reserved for General Relativity handbooks. In these notes an analysis of the effect of such forces in a classical (newtonian) context is made, as well as a study of the relation between the precession of the Foucault pendulum and the holonomy on a surface, including some critical remarks about the common statement \textquotedblleft precession of Foucault pendulum equals holonomy on the sphere\textquotedblright.