Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 2, pp. 427466 (2010) 

Blockdiagonalized rigidity matrices of symmetric frameworks and applicationsBernd SchulzeInstitut of Mathematics, MA 62, TU Berlin, D10623 Berlin, GermanyAbstract: In this paper, we give a complete selfcontained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a blockdiagonalized form using techniques from group representation theory. This theorem is basic to a number of useful and interesting results concerning the rigidity and flexibility of symmetric frameworks. As an example, we use this theorem to prove a generalization of the symmetryextended version of Maxwell's rule given in [FG] which can be applied to both injective and noninjective realizations in all dimensions. [FG] Fowler, P. W.; Guest, S. D.: A symmetry extension of Maxwell's rule for rigidity of frames. Int. J. Solids Struct. 37 (2000), 17931804. Full text of the article (for subscribers):
Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.
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