Coning, Symmetry and Spherical Frameworks
Coning, Symmetry and Spherical Frameworks
复制标题
圆锥、对称和球形框架
DOI：
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发表时间：
2011
影响因子：
0.8
通讯作者：
W. Whiteley
中科院分区：
文献类型：
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作者：
B. Schulze;W. Whiteley
在本文中，我们联合收割机单独的工作（a）转移无穷小刚性的结果，从一个欧几里德空间到下一个更高的维锥（Whiteley在Topol。Struct.8：53-70，1983），（B）通过相关的刚性矩阵将这些结果进一步转移到球面空间（Saliola和Whiteley in arXiv：0709.3354，2007），以及（c）从对称无穷小运动预测有限运动，该运动在ArXiv导出的轨道刚性矩阵的规则点处（Schulze和Whiteley in Discrete Comput. 46：561-598，2011）。每一种技术都经过了重新设计和简化，可以应用于多个度量，包括闵可夫斯基度量$mathbb{M}^{d}$和双曲度量$mathbb{E}^{d}$，$mathbb {E}^{d+1}$，$mathbb{S}^{d}$，$mathbb{M}^{d}$和$mathbb{E}^{d}$中相应对称框架下的无穷小和有限运动。我们还考虑了与其他Cayley-Klein几何覆盖在共享的基础射影几何的进一步扩展。
In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning (Whiteley in Topol. Struct. 8:53–70, 1983), (b) the further transfer of these results to spherical space via associated rigidity matrices (Saliola and Whiteley in arXiv:0709.3354, 2007), and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix (Schulze and Whiteley in Discrete Comput. Geom. 46:561–598, 2011). Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric $mathbb{M}^{d}$ and the hyperbolic metric ℍd.This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among $mathbb{E}^{d}$, cones in $mathbb{E}^{d+1}$, $mathbb{S}^{d}$, $mathbb{M}^{d}$, and ℍd. We also consider the further extensions associated with the other Cayley–Klein geometries overlaid on the shared underlying projective geometry.