When is a planar rod configuration infinitesimally rigid?

We provide a way of determining the infinitesimal rigidity of rod configurations realizing a rank two incidence geometry in the Euclidean plane. We model each rod with a cone over its point set and prove that the resulting geometric realization of the incidence geometry is infinitesimally rigid in r...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Lundqvist, Signe, Stokes, Klara, Lars-Daniel Öhman
Format: Article
Language:English
Subjects:
Configurations
Euclidean geometry
Online Access:Get full text
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Summary:We provide a way of determining the infinitesimal rigidity of rod configurations realizing a rank two incidence geometry in the Euclidean plane. We model each rod with a cone over its point set and prove that the resulting geometric realization of the incidence geometry is infinitesimally rigid in regular position if and only if the resulting cone graph is infinitesimally rigid in generic position. This is a generalization of the Molecular conjecture.
ISSN:2331-8422