  We discuss the rolling, without slip and without twist, of Stiefel manifolds
equipped with $\alpha$-metrics, from an intrinsic and an extrinsic point of
view. We, however, start with a more general perspective, namely by
investigating intrinsic rolling of normal naturally reductive homogeneous
spaces. This gives evidence why a seemingly straightforward generalization of
intrinsic rolling of symmetric spaces to normal naturally reductive homogeneous
spaces is not possible, in general. For a given control curve, we derive a
system of explicit time-variant ODEs whose solutions describe the desired
rolling. These findings are applied to obtain the intrinsic rolling of Stiefel
manifolds, which is then extended to an extrinsic one. Moreover, explicit
solutions of the kinematic equations are obtained provided that the development
curve is the projection of a not necessarily horizontal one-parameter subgroup.
In addition, our results are put into perspective with examples of rolling
Stiefel manifolds known from the literature.
