English

Equilibrium stresses and rigidity for infinite tensegrities and frameworks

Metric Geometry 2023-08-23 v3

Abstract

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.

Keywords

Cite

@article{arxiv.2207.14369,
  title  = {Equilibrium stresses and rigidity for infinite tensegrities and frameworks},
  author = {Stephen Power},
  journal= {arXiv preprint arXiv:2207.14369},
  year   = {2023}
}

Comments

Journal accepted version, to appear in the Journal of Mathematical Analysis and Applications. 19 pages, 8 figures. More detail and examples given. The implication "BPS implies BSR (boundedly smoothly rigid)" has been strengthened to "BPS implies DCR (directedly continuously rigid)"

R2 v1 2026-06-25T01:19:04.564Z