Figure 4
From: Resonantly excited precession motion of three-dimensional vortex core in magnetic nanospheres

Model for analytical derivations.
(a) Definition of spherical coordinates and local spherical reference frame (colored surface) for local magnetization m. (b) Schematic of model sphere wherein single rigid vortex core is pointed in direction of θ0 and ϕ0, as defined by the polar and azimuthal angle coordinates.