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

[img]
Preview
PDF (incid_sym_barjoint_STBS_Rev)
incid_sym_barjoint_STBS_Rev.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (453kB)

Abstract

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:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
75359
Deposited By:
Deposited On:
09 Sep 2015 06:29
Refereed?:
Yes
Published?:
Published
Last Modified:
30 Sep 2020 00:49