A note on stability of the vertical uniform rotations of the heavy top

TL;DR

This paper addresses the stability of vertical uniform rotations of a heavy top, providing a complete solution using linearization and conserved quantities of the system.

Contribution

It offers a comprehensive analysis of the stability problem for vertical rotations of a heavy top, utilizing linearization and conserved quantities.

Findings

Stability of vertical rotations is fully characterized.

Linearization method effectively analyzes stability.

Conserved quantities are key to the stability analysis.

Abstract

We prove that the stability problem of a vertical uniform rotation of a heavy top is completely solved by using the linearization method and the conserved quantities of the differential system which describe the rotation of the heavy top.