Home > Research > Publications & Outputs > Rigidity of linearly constrained frameworks

Electronic data

  • LIN_constrained_frameworks_rigid_26_06_18

    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices, Volume 2020, Issue 12, June 2020, Pages 3824–3840, https://doi.org/10.1093/imrn/rny170 is available online at: https://academic.oup.com/imrn/article-abstract/2020/12/3824/5067960

    Accepted author manuscript, 319 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

View graph of relations

Rigidity of linearly constrained frameworks

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
Close
<mark>Journal publication date</mark>1/06/2020
<mark>Journal</mark>International Mathematics Research Notices
Issue number12
Volume2020
Number of pages17
Pages (from-to)3824-3840
Publication StatusPublished
Early online date8/08/18
<mark>Original language</mark>English

Abstract

We consider the problem of characterising the generic rigidity of bar-joint frameworks in R d in which each vertex is constrained to lie in a given affine subspace. The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010. We will extend their characterisation to the case when d ≥ 3 and each vertex is constrained to lie in an affine subspace of dimension t, when t = 1, 2 and also when t ≥ 3 and d ≥ t(t−1). We then point out that results on body-bar frameworks obtained by N. Katoh and S. Tanigawa in 2013 can be used to characterise when a graph has a rigid realisation as a d-dimensional body-bar framework with a given set of linear constraints.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The definitive publisher-authenticated version James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon, Rigidity of Linearly Constrained Frameworks, International Mathematics Research Notices, Volume 2020, Issue 12, June 2020, Pages 3824–3840, https://doi.org/10.1093/imrn/rny170 is available online at: https://academic.oup.com/imrn/article-abstract/2020/12/3824/5067960