Balancing a vertical stick on a stochastically driven horizontal plate : a variation on the Kapitza effect

TL;DR

This paper investigates how stochastic horizontal vibrations, modeled as colored noise, can stabilize a vertical stick balancing on a moving plate, revealing conditions under which the stick remains upright.

Contribution

It introduces a novel analysis of stochastic driving effects on the Kapitza-like stabilization of a vertical stick, emphasizing the role of noise correlation strength.

Findings

Colored noise with sufficient correlation strength stabilizes the stick.

Stochasticity can prevent the fall of the stick under specific conditions.

The critical noise correlation strength determines stabilization.

Abstract

We consider the trick of balancing a vertical stick on a horizontal plate. It is shown that the horizontal stochastic driving of the point of contact can prevent the stick from falling provided that the stochasticity is that of a coloured noise with a correlation strength stronger than a critical value.