  We consider quantum brachistochrone evolution for a spin-$s$ system on
rotational manifolds. Such manifolds are determined by the rotation of the
eigenstates of the operator of projection of spin-$s$ on some direction. The
Fubini-Study metrics of these manifolds are those of spheres with radii
dependent on the value of the spin and on the value of the spin projection. The
conditions for optimal evolution of the spin-$s$ system on rotational manifolds
are obtained.
