带有平面曲线的等轴对称变形圆锥和圆柱
Isometrically deformable cones and cylinders carrying planar curves
摘要：
我们研究圆锥体和圆柱体的1参数等距变形进行至少两个平面曲线，保持平面在此连续屈曲，并位于非平行平面。我们调查这个几何/运动学的问题，在光滑和离散设置，因为它是一个广义的建设所谓的T-面拉链管的基础。在对比的圆柱形的情况下，可以很容易地解决，圆锥形的是更棘手的，但我们成功地给出了一个封闭的形式解决方案的离散的情况下，这是用来证明这些锥对应于帽的Bricard八面体的平面对称型。对于光滑的情况，我们能够减少问题的符号计算的手段，一个常微分方程，但其解决方案仍然是一个开放的问题。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
