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When is a planar rod configuration infinitesimally rigid?

2021/12/03 by Signe Lundqvist, Lundqvist, Signe, Klara Stokes +3
Biochemistry, Genetics and Molecular Biology · Engineering · #52C25 #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #Combinatorics (math.CO) #FOS: Mathematics #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2112.01960

openalex publication_date 2021/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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