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Rigidity of frameworks supported on surfaces

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Rigidity of frameworks supported on surfaces. / Nixon, Anthony; Owen, J. C.; Power, Stephen.
In: SIAM Journal on Discrete Mathematics, Vol. 26, No. 4, 2012, p. 1733-1757.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nixon, A, Owen, JC & Power, S 2012, 'Rigidity of frameworks supported on surfaces', SIAM Journal on Discrete Mathematics, vol. 26, no. 4, pp. 1733-1757. https://doi.org/10.1137/110848852

APA

Nixon, A., Owen, J. C., & Power, S. (2012). Rigidity of frameworks supported on surfaces. SIAM Journal on Discrete Mathematics, 26(4), 1733-1757. https://doi.org/10.1137/110848852

Vancouver

Nixon A, Owen JC, Power S. Rigidity of frameworks supported on surfaces. SIAM Journal on Discrete Mathematics. 2012;26(4):1733-1757. doi: 10.1137/110848852

Author

Nixon, Anthony ; Owen, J. C. ; Power, Stephen. / Rigidity of frameworks supported on surfaces. In: SIAM Journal on Discrete Mathematics. 2012 ; Vol. 26, No. 4. pp. 1733-1757.

Bibtex

@article{1077c361a7dd4e6ba4762aceb5ac2873,
title = "Rigidity of frameworks supported on surfaces",
abstract = "A theorem of Laman gives a combinatorial characterisation of the graphs thatadmit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.",
keywords = "bar-joint framework, framework on a surface , rigid framework",
author = "Anthony Nixon and Owen, {J. C.} and Stephen Power",
year = "2012",
doi = "10.1137/110848852",
language = "English",
volume = "26",
pages = "1733--1757",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

RIS

TY - JOUR

T1 - Rigidity of frameworks supported on surfaces

AU - Nixon, Anthony

AU - Owen, J. C.

AU - Power, Stephen

PY - 2012

Y1 - 2012

N2 - A theorem of Laman gives a combinatorial characterisation of the graphs thatadmit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.

AB - A theorem of Laman gives a combinatorial characterisation of the graphs thatadmit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are constrained to move on a two-dimensional smooth submanifold $\M$. Furthermore, when $\M$ is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.

KW - bar-joint framework

KW - framework on a surface

KW - rigid framework

U2 - 10.1137/110848852

DO - 10.1137/110848852

M3 - Journal article

VL - 26

SP - 1733

EP - 1757

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 4

ER -