Frameworks symmetry and rigidity

Owen, J. C. and Power, Stephen (2010) Frameworks symmetry and rigidity. International Journal of Computational Geometry and Applications, 20 (6). pp. 723-750. ISSN 0218-1959

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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.

Item Type:
Journal Article
Journal or Publication Title:
International Journal of Computational Geometry and Applications
Additional Information:
The paper was published in December 2010. (No record of acceptance date.)
Uncontrolled Keywords:
?? bar-joint frameworksymmetryrigidity computational theory and mathematicscomputational mathematicsgeometry and topologytheoretical computer scienceapplied mathematics ??
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Deposited On:
09 Sep 2015 06:34
Last Modified:
29 Feb 2024 00:49