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On the Controllability of the Rolling Problem onto the Hyperbolic n-space.

Abstract : In the present paper, we study the controllability of the control system associated to rolling without slipping or spinning of a Riemannian manifold (M, g) onto the hyperbolic n-space H n. Our main result states that the system is completely controllable if and only if (M, g) 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 control-lability issue in this case reduces to determine whether (M, g) admits a reducible action of a hyperbolic analog of the holonomy group and a well-known fact about connected subgroups of O(n, 1) acting irreducibly on the Lorentzian space R n,1 .
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Yacine Chitour, M.-G. Molina, Petri Kokkonen. On the Controllability of the Rolling Problem onto the Hyperbolic n-space.. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.948-968. ⟨10.1137/120901830⟩. ⟨hal-01271288⟩

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