Tue, 11/18/2014 -
10:00 to 12:00
In this thesis, we study the rolling motion without spinning nor slipping of a smooth manifold against another. The purpose is to find the necessary and sufficient conditions for the controllability issue of the rolling system. Firstly, we present a characterization of the state space of rolling Riemannian manifolds which their dimensions are not necessarly equal and of the development of affine manifolds of same dimension. We also state the definitions of rolling lifts and rolling distributions with respect to the previous notions. We show some controllability results of the rolling system of Riemannian manifolds. Then, we study the necessary conditions of non-controllability of the rolling of a 2-dimensional Riemannian manifold against a 3-dimensional Riemannian manifold. We prove that the dimension of an arbitrary non-open orbit of the state space belongs to {2,5,6,7}. The second part of my thesis addresses the issue of horizontal holonomy associated to smooth distribution on smooth affine connected manifold. We proved that the horizontal holonomy group is a Lie subgroup of GL(n) where n is the dimension of considered manifold. Then, we show by means of an example (free step-two homogeneous Carnot group) that the horizontal holonomy group is not necessarily equal to the holonomy group.

Composition du jury :

Directeurs de thèse :M. Yacine CHITOUR    (Uni. Paris-Sud, LSS) 

                              M. Ali WEHBE   (Uni. Libanaise)                              

Co-encadrant : Petri KOKKONEN   (Varian Medical Systems)                                 

Rapporteurs : Mme Irina MARKINA  (Uni. de Bergen)                         

                     M. Frédéric JEAN (ENSTA-ParisTech)                             

Examinateurs : Mme Dorothee NORMAND-CYROT (Uni. Paris-  Sud,LSS)                            

                        Mme Fátima SILVA-LEITE (Uni. de Coimbra)

                        M. Mohamad MEHDI  (Uni. Libanaise)