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- W2017149481 abstract "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." @default.
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- W2017149481 date "2014-09-23" @default.
- W2017149481 modified "2023-10-14" @default.
- W2017149481 title "Rolling Manifolds of Different Dimensions" @default.
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- W2017149481 doi "https://doi.org/10.1007/s10440-014-9972-2" @default.
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