2022/07/28 by Power, Stephen
#52C25 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2207.14369
Asymptotic equilibrium stresses are defined for countably infinite tensegrities and generalisations of the Roth-Whiteley characterisation of first-order rigidity are obtained. Generalisations of prestress stability and second order rigidity are given for countably infinite bar-joint frameworks and are shown to give sufficient conditions for continuous rigidity relative to certain prescribed motions. The proofs are based on a new short proof for finite frameworks that prestress stability ensures continuous rigidity.