Internal approximations of reachable sets of control systems with state constraints |
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Authors: | M. I. Gusev |
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Affiliation: | 1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia 2. Moscow State University, Moscow, 119991, Russia 3. Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol’shoi Karetnyi per. 19, Moscow, 127994, Russia
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Abstract: | We construct self-intersecting flexible cross-polytopes in the spaces of constant curvature, that is, in Euclidean spaces (mathbb{E}^n) , spheres (mathbb{S}^n) , and Lobachevsky spaces Λ n of all dimensions n. In dimensions n ≥ 5, these are the first examples of flexible polyhedra. Moreover, we classify all flexible cross-polytopes in each of the spaces (mathbb{E}^n) , (mathbb{S}^n) , and Λ n . For each type of flexible cross-polytopes, we provide an explicit parametrization of the flexion by either rational or elliptic functions. |
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