Infinitesimal rigidity for non-Euclidean bar-joint frameworks
Metric Geometry
2017-05-17 v2 Combinatorics
Abstract
The minimal infinitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R^2, ||.||_q) are characterised in terms of (2,2)-tight graphs. Specifically, a generically placed bar-joint framework (G,p) in the plane is minimally infinitesimally rigid with respect to a non-Euclidean l^q norm if and only if the underlying graph G = (V,E) contains 2|V|-2 edges and every subgraph H=(V(H),E(H)) contains at most 2|V(H)|-2 edges.
Cite
@article{arxiv.1304.3385,
title = {Infinitesimal rigidity for non-Euclidean bar-joint frameworks},
author = {Derek Kitson and Stephen Power},
journal= {arXiv preprint arXiv:1304.3385},
year = {2017}
}
Comments
This preprint version differs from the final version which is to appear in the Bulletin of the London Mathematical Society