  We study the phenomenon of spontaneous breaking of rotational symmetry (SBRS)
in the rotating solutions of two types of baby Skyrme models. In the first the
domain is a two-sphere and in the other, the Skyrmions are confined to the
interior of a unit disk. Numerical full-field results show that when the
angular momentum of the Skyrmions increases above a certain critical value, the
rotational symmetry of the solutions is broken and the minimal energy
configurations become less symmetric. We propose a possible mechanism as to why
SBRS is present in the rotating solutions of these models, while it is not
observed in the `usual' baby Skyrme model. Our results might be relevant for a
qualitative understanding of the non-spherical deformation of excited nucleons
with high orbital angular momentum.
