In his paper on Morse theory applied to the length function on Stiefel manifolds, Ramanujan [1] makes use of a particular embedding. This paper describes geometric properties of real Stiefel manifolds that arise from such embedding. In particular, Lie algebraic definitions of tangent and normal spaces lend themselves to study geodesic equation. We thus recover known integrals of motions that are easily derived in this embedding. Finally, we address issues arising from this embedding in solving the “rolling” problem.