Numerical study of Kapitza pendulum

TL;DR

This paper presents a numerical investigation of the Kapitza pendulum, exploring its stability and behavior across various regimes, and comparing results with known analytical solutions in limiting cases.

Contribution

It provides a comprehensive numerical analysis of the Kapitza pendulum's dynamics across different physical regimes, filling gaps where analytical solutions are unavailable.

Findings

Vertical stability achieved under specific conditions

Numerical results align with known analytical solutions in limiting cases

Demonstrates complex behavior of the pendulum under various oscillation parameters

Abstract

A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be obtained, such as the vertical position of the pendulum under certain conditions might become stable, no explicit analytical solution for the pendulum trajectory is known. We carry out a numerical study of Kapitza pendulum for a number of different physical regimes. Comparison is made with the limiting cases where the exact solution is known.