Stability of rotating magnetic levitation

TL;DR

This paper investigates the stability conditions of a rotating magnetic levitation system through theoretical modeling and experiments, highlighting the importance of damping and system parameters for achieving stable levitation.

Contribution

It provides a combined theoretical and experimental analysis of magnetic levitation stability, emphasizing the role of damping and system parameters in stability regions.

Findings

Damping is essential for stable levitation.

Stability regions depend on rotation speed and damping coefficients.

Theoretical predictions align qualitatively with experimental results.

Abstract

Dynamical magnetic levitation has attracted broad interest in the realm of physics and engineering. The stability analysis of such system is of great significance for practical applications. In this work, we investigate the stable magnetic levitation of a floater magnet above a rotating magnet and copper board system. The conditions for stable levitation are analyzed through both theoretical modeling and experimental observation. This study focuses on the interplay between magnetic forces, damping effects from the copper board, and rotational dynamics. We derive the equilibrium conditions, perform stability analysis, and present phase diagrams in parametric spaces of rotation speed and damping coefficients. The theoretical predictions show qualitative agreement with experimental results, particularly in demonstrating how damping is essential for stable levitation and how the stability region depends on the geometric and magnetic parameters of the system.