2017/07/07 by Ivan Izmestiev, Izmestiev, Ivan
Engineering · #Dynamics and Control of Mechanical Systems #Elasticity and Wave Propagation #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.1707.02172
openalex publication_date 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a survey article on the infinitesimal rigidity of frameworks in Euclidean, hyperbolic, and spherical geometry. We discuss the equivalence of the static and kinematic formulations of the infinitesimal rigidity, the projective interpretation of statics (representing forces as bivectors), and the infinitesimal Pogorelov maps that establish correspondence between infinitesimal motions of a framework and of its geodesic image. Also we describe the Maxwell-Cremona correspondence between equilibrium loads and polyhedral lifts, both for Euclidean and for non-Euclidean frameworks.