Infinitesimal Rigidity of Symmetric Frameworks
Abstract
We propose new symmetry-adapted rigidity matrices to analyze the infinitesimal rigidity of arbitrary-dimensional bar-joint frameworks 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 generic as possible subject to the symmetry constraints imposed by a reflection, a half-turn or a three-fold 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.
Cite
@article{arxiv.1308.6380,
title = {Infinitesimal Rigidity of Symmetric Frameworks},
author = {Bernd Schulze and Shin-ichi Tanigawa},
journal= {arXiv preprint arXiv:1308.6380},
year = {2014}
}
Comments
The version 1 was split into two papers, and this version 2 consists of Sections 1 - 6 of the first version. The second part of the version 1 (Sections 7 and 8) is given in arXiv:1402.0039