Universal and Dimensional Rigidities

  • Abdo Y. Alfakih


In this chapter, we study the universal rigidity problem of bar frameworks and the related problem of dimensional rigidity. The main tools in tackling these two problems are the Cayley configuration spectrahedron \(\mathcal{F}\), defined in ( 8.10), and Ω, the stress matrix, defined in ( 8.13). The more general problem of universally linked pair of nonadjacent nodes is also studied and the results are interpreted in terms of the Strong Arnold Property and the notion of nondegeneracy in semidefinite programming.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Abdo Y. Alfakih
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of WindsorWindsorCanada

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