Rigidity of Linearly Constrained Frameworks
Rigidity of Linearly Constrained Frameworks
复制标题
线性约束框架的刚性
DOI：
10.1093/imrn/rny170
复制
发表时间：
2018
影响因子：
1
通讯作者：
A. Nixon
中科院分区：
文献类型：
--
作者：
J. Cruickshank;H. Guler;B. Jackson;A. Nixon
我们考虑了$\mathbb{R}^d$中每个顶点都被约束在给定仿射子空间中的杆节点框架的一般刚度的刻画问题。$d=2$的特殊情况之前由Streinu和Theran b[14]在2010年解决。我们将把它们的特征扩展到$d\geq 3$和每个顶点被约束在维度为$t$的仿射子空间中的情况，当$t=1,2$和$t\geq 3$和$d\geq t(t-1)$时。然后我们指出，2013年由Katoh和Tanigawa[8]获得的关于体杆框架的结果可用于表征图何时具有具有给定一组线性约束的$d$维体杆框架的刚性实现。
We consider the problem of characterising the generic rigidity of bar-joint frameworks in $\mathbb{R}^d$ in which each vertex is constrained to lie in a given affine subspace. The special case when $d=2$ was previously solved by Streinu and Theran [14] in 2010. We will extend their characterisation to the case when $d\geq 3$ and each vertex is constrained to lie in an affine subspace of dimension $t$, when $t=1,2$ and also when $t\geq 3$ and $d\geq t(t-1)$. We then point out that results on body–bar frameworks obtained by Katoh and Tanigawa [8] in 2013 can be used to characterise when a graph has a rigid realisation as a $d$-dimensional body–bar framework with a given set of linear constraints.
点超平面框架、滑块关节和刚度保持变换
DOI：
10.1016/j.jctb.2018.07.008
发表时间：
2019
期刊：
Journal of Combinatorial Theory, Series B
影响因子：
--
作者：
Eftekhari Y
通讯作者：
Eftekhari Y