Rigidity of Frameworks Supported on Surfaces
Rigidity of Frameworks Supported on Surfaces
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表面支撑框架的刚性
DOI：
10.1137/110848852
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Power
中科院分区：
文献类型：
--
作者：
A. Nixon;J. Owen;S. Power
一个定理的拉曼给出了一个组合表征的图形，承认实现作为一个最低限度的刚性通用酒吧联合框架在$\bR^2 $。一个更一般的理论是开发的框架在$\bR^3$，其顶点被约束到移动的二维光滑子流形$\M$。当$\M$是同心球的并集、平行平面的并集或同心圆柱的并集时，得到了一般框架的最小刚度的充分必要组合条件.
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.