Infinitesimal Rigidity of Symmetric Frameworks
arXiv:1308.6380
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.
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
References in corpus (5)
- Block-diagonalized rigidity matrices of symmetric frameworks and applications
- Generic rigidity of frameworks with orientation-preserving crystallographic symmetry
- Generic rigidity of reflection frameworks
- Matroids of Gain Graphs in Applied Discrete Geometry
- Henneberg constructions and covers of cone-Laman graphs