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Frameworks symmetry and rigidity

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Frameworks symmetry and rigidity. / Owen, J. C.; Power, Stephen.
In: International Journal of Computational Geometry and Applications, Vol. 20, No. 6, 12.2010, p. 723-750.

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

Harvard

Owen, JC & Power, S 2010, 'Frameworks symmetry and rigidity', International Journal of Computational Geometry and Applications, vol. 20, no. 6, pp. 723-750. https://doi.org/10.1142/S0218195910003505

APA

Owen, J. C., & Power, S. (2010). Frameworks symmetry and rigidity. International Journal of Computational Geometry and Applications, 20(6), 723-750. https://doi.org/10.1142/S0218195910003505

Vancouver

Owen JC, Power S. Frameworks symmetry and rigidity. International Journal of Computational Geometry and Applications. 2010 Dec;20(6):723-750. doi: 10.1142/S0218195910003505

Author

Owen, J. C. ; Power, Stephen. / Frameworks symmetry and rigidity. In: International Journal of Computational Geometry and Applications. 2010 ; Vol. 20, No. 6. pp. 723-750.

Bibtex

@article{84ae81fa4b7f4ce48acfa5650df59f5e,
title = "Frameworks symmetry and rigidity",
abstract = "Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in ℝd. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.",
keywords = "Bar-joint framework, Symmetry, Rigidity ",
author = "Owen, {J. C.} and Stephen Power",
note = "The paper was published in December 2010. (No record of acceptance date.)",
year = "2010",
month = dec,
doi = "10.1142/S0218195910003505",
language = "English",
volume = "20",
pages = "723--750",
journal = "International Journal of Computational Geometry and Applications",
issn = "0218-1959",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "6",

}

RIS

TY - JOUR

T1 - Frameworks symmetry and rigidity

AU - Owen, J. C.

AU - Power, Stephen

N1 - The paper was published in December 2010. (No record of acceptance date.)

PY - 2010/12

Y1 - 2010/12

N2 - Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in ℝd. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.

AB - Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in ℝd. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.

KW - Bar-joint framework

KW - Symmetry

KW - Rigidity

U2 - 10.1142/S0218195910003505

DO - 10.1142/S0218195910003505

M3 - Journal article

VL - 20

SP - 723

EP - 750

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

SN - 0218-1959

IS - 6

ER -