Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 2, pp. 427-466 (2010)
Block-diagonalized rigidity matrices of symmetric frameworks and applications
Bernd SchulzeInstitut of Mathematics, MA 6-2, TU Berlin, D-10623 Berlin, Germany
Abstract: In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized 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 symmetry-extended version of Maxwell's rule given in [FG] which can be applied to both injective and non-injective 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), 1793--1804.
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Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.