Graphs and Combinatorial Optimization: from Theory to Applications - CTW 2023, Garmisch-Partenkirchen, Germany, June 20-22
Graphs and Combinatorial Optimization: from Theory to Applications - CTW 2023, Garmisch-Partenkirchen, Germany, June 20-22
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图和组合优化：从理论到应用 - CTW 2023，德国加米施-帕滕基兴，6 月 20-22 日
DOI：
10.1007/978-3-031-46826-1_4
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发表时间：
2024
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影响因子：
--
通讯作者：
Hewetson J
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作者：
Hewetson J
考虑 3 维空间中约束位于球体联合上的杆接头框架的刚性。众所周知，单个球体上的刚度相当于欧几里得刚度，并且这种等价性延伸到球体同心的情况。我们考虑当球体具有不同的中心并给出彩色稀疏条件时的情况，类似于欧几里得的情况，对于具有不同中心的两个球体的并集的通用框架是刚性的是必要的。我们证明这些条件一般来说是不够的，并添加了我们证明在特殊情况下足够的附加条件。
Consider the rigidity of bar-joint frameworks in 3-dimensional space that are constrained to lie on a union of spheres. It is well known that rigidity on a single sphere is equivalent to Euclidean rigidity and this equivalence extends to the case where the spheres are concentric. We consider the case when the spheres have distinct centres and give coloured sparsity conditions, analogous to the Euclidean case, necessary for a generic framework on the union of two spheres with different centres to be rigid. We show that these conditions are not sufficient in general and add additional conditions which we prove are sufficient in a special case.