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  • JacksonNixonStressMatrices

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Stress matrices and global rigidity of frameworks on surfaces

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>10/2015
<mark>Journal</mark>Discrete and Computational Geometry
Issue number3
Volume54
Number of pages24
Pages (from-to)586-609
Publication StatusPublished
Early online date20/08/15
<mark>Original language</mark>English

Abstract

In 2005, Bob Connelly showed that a generic framework in R d is globally rigid if it has a stress matrix of maximum possible rank, and that this sufficient condition for generic global rigidity is preserved by the 1-extension operation. His results gave a key step in the characterisation of generic global rigidity in the plane. We extend these results to frameworks on surfaces in R 3 . For a framework on a family of concentric cylinders, cones or ellipsoids, we show that there is a natural surface stress matrix arising from assigning edge and vertex weights to the framework, in equilibrium at each vertex. In the case of cylinders and ellipsoids, we show that having a maximum-rank stress matrix is sufficient to guarantee generic global rigidity on the surface. We then show that this sufficient condition for generic global rigidity is preserved under 1-extension and use this to make progress on the problem of characterising generic global rigidity on the cylinder.

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Evidence of acceptance is on publisher pdf The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-015-9724-8