%0 Journal Article %T Rolling Against a Sphere The Non-transitive Case %+ Laboratoire des signaux et systèmes (L2S) %+ Department of Mathematics [Bergen] (UiB) %+ Universidad de la frontera [Chile] %A Chitour, Yacine %A Godoy Molina, Mauricio %A Kokkonen, Petri %A Markina, Irina %Z iCODE institute, research project of the Idex Paris-Saclay %Z Norwegian Research CouncilResearch Council of Norway [NFR-FRINAT 213440/BG, NFR ISP 239033/F20] %< avec comité de lecture %@ 1050-6926 %J The Journal of Geometric Analysis %I Springer %V 26 %N 4 %P 2542-2562 %8 2016 %D 2016 %R 10.1007/s12220-015-9638-y %K Rolling system %K Sasakian manifold %K 3-Sasakian manifold %K Nonholonomic mechanics %K Holonomy of connections %Z Engineering Sciences [physics]/AutomaticJournal articles %X We study the control system of a Riemannian manifold M of dimension n rolling on the sphere . The controllability of this system is described in terms of the holonomy of a vector bundle connection which, we prove, is isomorphic to the Riemannian holonomy group of the cone C(M) of M. Using Berger's list, we reduce the possible holonomies to a few families. In particular, we focus on the cases where the holonomy is the unitary and the symplectic group. In the first case, using the rolling formalism, we construct explicitly a Sasakian structure on M; and in the second case, we construct a 3-Sasakian structure on M. %G English %2 https://centralesupelec.hal.science/hal-02307514/document %2 https://centralesupelec.hal.science/hal-02307514/file/pdf%20de%20rolling%20against%20a%20sphere.pdf %L hal-02307514 %U https://centralesupelec.hal.science/hal-02307514 %~ CNRS %~ UNIV-PSUD %~ SUP_LSS %~ SUP_SYSTEMES %~ CENTRALESUPELEC %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ UNIV-PSUD-SACLAY %~ CENTRALESUPELEC-SACLAY %~ GS-ENGINEERING %~ GS-COMPUTER-SCIENCE