Controllability of the rolling system of a Lorentzian manifold on ${\mathbb R}^{n,1}$
| Autor: | Osses, Abraham Bobadilla, Molina, Mauricio Godoy |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study the mechanical system associated with rolling a Lorentzian manifold $(M,g)$ of dimension $n+1\geq2$ on flat Lorentzian space $\widehat{M}={\mathbb R}^{n,1}$, without slipping or twisting. Using previous results, it is known that there exists a distribution $\mathcal{D}_R$ of rank $(n+1)$ defined on the configuration space $Q(M,\widehat{M})$ of the rolling system, encoding the no-slip and no-twist conditions. Our objective is to study the problem of complete controllability of the control system associated with $\mathcal{D}_R$. The key lies in examining the holonomy group of the distribution $\mathcal{D}_R$ and, following the approach of \cite{ChKok}, establishing that the rolling problem is completely controllable if and only if the holonomy group of $(M,g)$ equals $SO_0(n,1)$. Comment: 13 pages |
| Databáze: | arXiv |
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