Rigidity of linearly constrained frameworks

Cruickshank, James and Guler, Hakan and Jackson, Bill and Nixon, Anthony Keith (2018) Rigidity of linearly constrained frameworks. International Mathematics Research Notices. ISSN 1073-7928

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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.

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Journal Article
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International Mathematics Research Notices
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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, , rny170, https://doi.org/10.1093/imrn/rny170 is available online at:
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12 Jul 2018 13:50
Last Modified:
05 Apr 2020 05:06