Block-diagonalized rigidity matrices of symmetric frameworks and applications

Schulze, Bernd (2010) Block-diagonalized rigidity matrices of symmetric frameworks and applications. Contributions to Algebra and Geometry, 51 (2). pp. 427-466. ISSN 2191-0383

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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.

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Journal Article
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Contributions to Algebra and Geometry
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25 Apr 2013 12:20
Last Modified:
21 Nov 2022 23:35