2008/12/19 by J. C. Owen, S. C. Power, Owen, J. C. +1
Biochemistry, Genetics and Molecular Biology · Engineering · #20C99 #70C20 #Advanced Materials and Mechanics #Cellular Mechanics and Interactions #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.0812.3785
openalex publication_date 2008/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.