830 research outputs found
Iterative Universal Rigidity
A bar framework determined by a finite graph and configuration in
space is universally rigid if it is rigid in any . We provide a characterization of universally rigidity for any
graph and any configuration in terms of a sequence of affine
subsets of the space of configurations. This corresponds to a facial reduction
process for closed finite dimensional convex cones.Comment: 41 pages, 12 figure
Characterizing the universal rigidity of generic frameworks
A framework is a graph and a map from its vertices to E^d (for some d). A
framework is universally rigid if any framework in any dimension with the same
graph and edge lengths is a Euclidean image of it. We show that a generic
universally rigid framework has a positive semi-definite stress matrix of
maximal rank. Connelly showed that the existence of such a positive
semi-definite stress matrix is sufficient for universal rigidity, so this
provides a characterization of universal rigidity for generic frameworks. We
also extend our argument to give a new result on the genericity of strict
complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio
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