论文标题
表征通用张力的普遍刚性
Characterizing the Universal Rigidity of Generic Tensegrities
论文作者
论文摘要
紧张是由电缆，支撑杆和硬条制成的结构。如果在任何尺寸$ d'$中，$ d $二维时girty是普遍刚性的。由于康纳利（Connelly）而引起的著名的超稳定性条件提供了足够的条件，使紧张关系普遍僵化。戈特勒（Gortler）和瑟斯顿（Thurston）表明，当点配置为通用时，超稳定性表征了通用刚度，并且每个成员都是僵硬的条。我们将此结果扩展到两个方向。我们首先表明，通用的普遍刚性紧张是超级稳定的。然后，我们将其扩展到具有点组对称性的时态，并表明，只要张力是通用的模量对称性，这种表征仍然存在。我们的策略基于对称半决赛编程问题的块 - 划分技术，而我们的证明依赖于有限群体的真实不可约说明的理论。
A tensegrity is a structure made from cables, struts and stiff bars. A $d$-dimensional tensegirty is universally rigid if it is rigid in any dimension $d'$ with $d'\geq d$. The celebrated super stability condition due to Connelly gives a sufficient condition for a tensegrity to be universally rigid. Gortler and Thurston showed that super stability characterizes universal rigidity when the point configuration is generic and every member is a stiff bar. We extend this result in two directions. We first show that a generic universally rigid tensegrity is super stable. We then extend it to tensegrities with point group symmetry, and show that this characterization still holds as long as a tensegrity is generic modulo symmetry. Our strategy is based on the block-diagonalization technique for symmetric semidefinite programming problems, and our proof relies on the theory of real irreducible representation of finite groups.
