Resonances in the heavy symmetrical top with vibrating pivot

TL;DR

This paper investigates the resonance phenomena in a heavy symmetrical top with a vibrating pivot, deriving a criterion for when the top loses stability due to these vibrations.

Contribution

It introduces a new resonance criterion for a symmetrical top with a vibrating pivot, expanding understanding of stability under dynamic support conditions.

Findings

Resonance occurs at specific vibration frequencies.

Derived a mathematical criterion for resonance.

Identified conditions leading to loss of stability.

Abstract

In this work we consider a heavy symmetrical top whose pivot is subjected to vertical and horizontal vibrations, and derive a resonance criterion when the top is thrown off the stable position.