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Rigidity of frameworks on spheres

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

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Rigidity of frameworks on spheres. / Hewetson, John; Nixon, Anthony.
Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. ed. / Andreas Brieden; Stefan Pickl; Markus Siegle. Cham: Springer, 2024. p. 41-52 (AIRO Springer Series; Vol. 13).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Harvard

Hewetson, J & Nixon, A 2024, Rigidity of frameworks on spheres. in A Brieden, S Pickl & M Siegle (eds), Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. AIRO Springer Series, vol. 13, Springer, Cham, pp. 41-52. https://doi.org/10.1007/978-3-031-46826-1_4

APA

Hewetson, J., & Nixon, A. (2024). Rigidity of frameworks on spheres. In A. Brieden, S. Pickl, & M. Siegle (Eds.), Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023 (pp. 41-52). (AIRO Springer Series; Vol. 13). Springer. https://doi.org/10.1007/978-3-031-46826-1_4

Vancouver

Hewetson J, Nixon A. Rigidity of frameworks on spheres. In Brieden A, Pickl S, Siegle M, editors, Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. Cham: Springer. 2024. p. 41-52. (AIRO Springer Series). doi: 10.1007/978-3-031-46826-1_4

Author

Hewetson, John ; Nixon, Anthony. / Rigidity of frameworks on spheres. Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. editor / Andreas Brieden ; Stefan Pickl ; Markus Siegle. Cham : Springer, 2024. pp. 41-52 (AIRO Springer Series).

Bibtex

@inbook{c777dc2eff7a4ba18412df6cf8438560,
title = "Rigidity of frameworks on spheres",
abstract = "Consider the rigidity of bar-joint frameworks in 3-dimensional space that are constrained to lie on a union of spheres. It is well known that rigidity on a single sphere is equivalent to Euclidean rigidity and this equivalence extends to the case where the spheres are concentric. We consider the case when the spheres have distinct centres and give coloured sparsity conditions, analogous to the Euclidean case, necessary for a generic framework on the union of two spheres with different centres to be rigid. We show that these conditions are not sufficient in general and add additional conditions which we prove are sufficient in a special case.",
author = "John Hewetson and Anthony Nixon",
year = "2024",
month = feb,
day = "23",
doi = "10.1007/978-3-031-46826-1_4",
language = "English",
isbn = "9783031468254",
series = "AIRO Springer Series",
publisher = "Springer",
pages = "41--52",
editor = "Andreas Brieden and Stefan Pickl and Markus Siegle",
booktitle = "Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023",

}

RIS

TY - CHAP

T1 - Rigidity of frameworks on spheres

AU - Hewetson, John

AU - Nixon, Anthony

PY - 2024/2/23

Y1 - 2024/2/23

N2 - Consider the rigidity of bar-joint frameworks in 3-dimensional space that are constrained to lie on a union of spheres. It is well known that rigidity on a single sphere is equivalent to Euclidean rigidity and this equivalence extends to the case where the spheres are concentric. We consider the case when the spheres have distinct centres and give coloured sparsity conditions, analogous to the Euclidean case, necessary for a generic framework on the union of two spheres with different centres to be rigid. We show that these conditions are not sufficient in general and add additional conditions which we prove are sufficient in a special case.

AB - Consider the rigidity of bar-joint frameworks in 3-dimensional space that are constrained to lie on a union of spheres. It is well known that rigidity on a single sphere is equivalent to Euclidean rigidity and this equivalence extends to the case where the spheres are concentric. We consider the case when the spheres have distinct centres and give coloured sparsity conditions, analogous to the Euclidean case, necessary for a generic framework on the union of two spheres with different centres to be rigid. We show that these conditions are not sufficient in general and add additional conditions which we prove are sufficient in a special case.

U2 - 10.1007/978-3-031-46826-1_4

DO - 10.1007/978-3-031-46826-1_4

M3 - Chapter (peer-reviewed)

SN - 9783031468254

T3 - AIRO Springer Series

SP - 41

EP - 52

BT - Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023

A2 - Brieden, Andreas

A2 - Pickl, Stefan

A2 - Siegle, Markus

PB - Springer

CY - Cham

ER -