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