caa a22 4500 606166297 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10440-014-9972-2 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9972-2 Rolling Manifolds of Different Dimensions [Elektronische Daten] [Amina Mortada, Petri Kokkonen, Yacine Chitour] If (M,g) and $(\hat{M},\hat{g})$ are two smooth connected complete oriented Riemannian manifolds of dimensions n and $\hat{n}$ respectively, we model the rolling of (M,g) onto $(\hat{M},\hat{g})$ as a driftless control affine systems describing two possible constraints of motion: the first rolling motion (Σ) NS captures the no-spinning condition only and the second rolling motion (Σ) R corresponds to rolling without spinning nor slipping. Two distributions of dimensions $(n + \hat{n})$ and n are then associated to the rolling motions (Σ) NS and (Σ) R respectively. This generalizes the rolling problems considered in Chitour and Kokkonen (Rolling manifolds and controllability: the 3D case, 2012) where both manifolds had the same dimension. The controllability issue is then addressed for both (Σ) NS and (Σ) R and completely solved for (Σ) NS . As regards to (Σ) R , basic properties for the reachable sets are provided as well as the complete study of the case $(n,\hat{n})=(3,2)$ and some sufficient conditions for non-controllability. Springer Science+Business Media Dordrecht, 2014 Riemannian geometry nationallicence Connection nationallicence Curvature tensor nationallicence Development nationallicence Rolling manifolds nationallicence Mortada Amina CNRS and STITS, Université Paris-Sud 11, 91192, Gif-sur-Yvette, France aut Kokkonen Petri Helsinki, Finland aut Chitour Yacine CNRS and Supélec, Université Paris-Sud 11, 91192, Gif-sur-Yvette, France aut Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 105-131 0167-8019 139:1<105 2015 139 10440 https://doi.org/10.1007/s10440-014-9972-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9972-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mortada Amina CNRS and STITS, Université Paris-Sud 11, 91192, Gif-sur-Yvette, France aut NATIONALLICENCE 700 1- Kokkonen Petri Helsinki, Finland aut NATIONALLICENCE 700 1- Chitour Yacine CNRS and Supélec, Université Paris-Sud 11, 91192, Gif-sur-Yvette, France aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 105-131 0167-8019 139:1<105 2015 139 10440