Infinitesimal rigidity of symmetric bar-joint frameworks

Schulze, Bernd and Tanigawa, Shin-ichi (2015) Infinitesimal rigidity of symmetric bar-joint frameworks. SIAM Journal on Discrete Mathematics, 29 (3). pp. 1259-1286. ISSN 0895-4801

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We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of bar-joint frameworks of arbitrary-dimension with Abelian point group symmetries. These matrices define new symmetry-adapted rigidity matroids on group-labeled quotient graphs. Using these new tools, we establish combinatorial characterizations of infinitesimally rigid two-dimensional bar-joint frameworks whose joints are positioned as generically as possible subject to the symmetry constraints imposed by a reflection, a half-turn, or a threefold rotation in the plane. For bar-joint frameworks which are generic with respect to any other cyclic point group in the plane, we provide a number of necessary conditions for infinitesimal rigidity.

Item Type:
Journal Article
Journal or Publication Title:
SIAM Journal on Discrete Mathematics
Additional Information:
Date of Acceptance: 06/05/2015
Uncontrolled Keywords:
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Deposited On:
09 Sep 2015 06:29
Last Modified:
04 Mar 2024 00:55