2022/12/11 by Georg Nawratil, Nawratil, Georg
Mathematics · Engineering · #Mathematics and Applications #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2212.05484
We study cones and cylinders with a 1-parametric isometric deformation carrying at least two planar curves, which remain planar during this continuous flexion and are located in non-parallel planes. We investigate this geometric/kinematic problem in the smooth and the discrete setting, as it is the base for a generalized construction of so-called T-hedral zipper tubes. In contrast to the cylindrical case, which can be solved easily, the conical one is more tricky, but we succeed to give a closed form solution for the discrete case, which is used to prove that these cones correspond to caps of Bricard octahedra of the plane-symmetric type. For the smooth case we are able to reduce the problem by means of symbolic computation to an ordinary differential equation, but its solution remains an open problem.