Arbitrarily close equilibrium orientations of magnetically levitated platforms

Abstract

In this paper, the equilibrium orientations of magnetically suspended platforms that are statically loaded and constrained to 2 degrees of freedom are analyzed. It is shown that under these conditions, a symmetric, 2-magnet system can have a maximum of two equilibrium orientations for a given force-moment load. Further, it is shown that these two equilibrium orientations can exist arbitrarily close to each other under certain conditions. The conditions for arbitrarily close equilibrium orientations are analyzed, and verified to be physically achievable with numeric examples. The findings are presented as a consideration for acceptable operating loads for magnetically levitated platforms with zero-power control.