Petri Kokkonen

On the Controllability of the Rolling Problem onto the Hyperbolic

In the present paper, we study the controllability of the control system associated with rolling without slipping or spinning of a Riemannian manifold

n

(M,g)

-space

onto the hyperbolic

Rolling of Manifolds and Controllability in dimension three

n

The rolling problem: overview and challenges

-space

Rolling Against a Sphere: The Non-transitive Case

{\mathbb H}^n

Rolling Manifolds: Intrinsic Formulation and Controllability

. Our main result states that the system is completely controllable if and only if

Rolling manifolds on space forms

(M,g)

Symmetries of the rolling model

is not isometric to a warped product of a special form, in analogy to the classical de Rham decomposition theorem for Riemannian manifolds. The proof is based on the observations that the controllability issue in this case reduces to determining whether

Rolling of manifolds without spinning

(M,g)