2008/12/16 by Oleg Karpenkov, Karpenkov, Oleg · 1 citation
Engineering · Mathematics · #52C25 #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.0812.3050
openalex publication_date 2008/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadrangles is a Kokotsakis mesh. We express the infinitesimal flexibility condition in terms of Ceva and Menelaus theorems. Further we study semi-algebraic properties of the set of flexible meshes and give equations describing it. For 3x3-meshes we obtain flexibility conditions in terms of face angles.