  We study the dissipation of moving magnets in levitation above a
superconductor. The rotation motion is analyzed using optical tracking
techniques. It displays a remarkable regularity together with long damping time
up to several hours. The magnetic contribution to the damping is investigated
in detail by comparing 14 distinct magnetic configurations, and points towards
amplitude-dependent dissipation mechanisms. The non-linear dynamics of the
mechanical rotation motion is also revealed and described with an effective
Duffing model. The obtained picture of the coupling of levitating magnets to
their environment sheds light on their potential as ultra-low dissipation
mechanical oscillators for high precision physics.
