Necessary Conditions for the Generic Global Rigidity of Frameworks on Surfaces
Necessary Conditions for the Generic Global Rigidity of Frameworks on Surfaces
复制标题
表面框架通用整体刚性的必要条件
DOI：
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发表时间：
2013
影响因子：
0.8
通讯作者：
A. Nixon
中科院分区：
文献类型：
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作者：
B. Jackson;T. McCourt;A. Nixon
由于Hendrickson， Connelly和Jackson和Jordán在其各个部分的结果，提供了$${{mathbb {R}}}^2$$ R2中一般杆节点框架的整体刚度的纯组合特征。已知类似的条件不足以表征高维的一般全局刚度。最近，在$${mathbb {R}}^3$$ R3中，当顶点被约束在各种表面（如圆柱体和锥体）上时，已经获得了通用框架的拉曼型刚度特征。本文给出了圆柱、圆锥和椭球上一般框架整体刚度的Hendrickson必要条件的类似形式。
A result due in its various parts to Hendrickson, Connelly, and Jackson and Jordán, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in $${{mathbb {R}}}^2$$R2. The analogous conditions are known to be insufficient to characterise generic global rigidity in higher dimensions. Recently Laman-type characterisations of rigidity have been obtained for generic frameworks in $${mathbb {R}}^3$$R3 when the vertices are constrained to lie on various surfaces, such as the cylinder and the cone. In this paper we obtain analogues of Hendrickson’s necessary conditions for the global rigidity of generic frameworks on the cylinder, cone and ellipsoid.