The dynamics of a rotating ellipsoid

TL;DR

This paper provides a theoretical explanation for the axis-raising phenomenon observed in a spinning ellipsoid, like a hard-boiled egg, on a rough surface, using Lagrangian formalism to derive its equations of motion.

Contribution

It introduces a novel theoretical framework explaining the axis-raising motion of a spinning ellipsoid on a rough surface, supported by derived equations of motion.

Findings

Derivation of equations of motion using Lagrangian formalism.

Explanation of the axis raising phenomenon.

Insight into the dynamics of spinning ellipsoids on rough surfaces.

Abstract

An interesting physical phenomenon, which contradicts our common sense, is concerned with the dynamics of motion of a spinning ellipsoid in a non smooth surface. A hard-boiled egg spinning on a table with a rough surface is an example. In this article, we present a theoretical explanation, of the dynamics of motion of this ellipsoid, that describes the axis raising phenomenon, from the horizontal to the vertical. The equations of motion were obtained with Lagrangian formalism.