Rolling Stiefel manifolds. (English) Zbl 1168.53007

Rolling maps and the corresponding kinematic equations are closely related to certain differential geometric constructions, i.e. to the so-called parallel transport of tangent vectors along arbitrary smooth curves on a manifold and therefore to the concept of geodesics. They also play an important role in certain optimal control and controllability problems. The present paper considers rolling maps for real Stiefel manifolds, which being the set of all orthonormal \(k\)-frames of an \(n\)-dimensional real Euclidean space are compact manifolds. They are considered as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the body in the usual way. The kinematic equations describing this rolling motion are derived.


53A17 Differential geometric aspects in kinematics
93B27 Geometric methods
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