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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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.

Item Type:
Journal Article
Journal or Publication Title:
Contributions to Algebra and Geometry
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
ID Code:
63636
Deposited By:
Deposited On:
25 Apr 2013 12:20
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Sep 2020 01:43