The Rigid Unit Mode spectrum for symmetric frameworks
Abstract
We establish several fundamental properties of the Rigid Unit Mode (RUM) spectrum for symmetric frameworks with a discrete abelian symmetry group and arbitrary linear constraints. In particular, we identify a nonempty subset of the RUM spectrum which derives from the joint eigenvalues of generators for the linear part of the symmetry group. These joint eigenvalues give rise to χ -symmetric flexes which span the space of translations for the framework. We show that the RUM spectrum is a union of Bohr-Fourier spectra arising from twisted almost periodic flexes of the framework. We also characterise frameworks for which every almost periodic flex is a translation.
Fields of Study & Subjects
Quantum Mechanics and Non-Hermitian Physics
Nonlinear Photonic Systems
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 566
- Issue
- 1
- Pages
- 131029–131029
- Publication date
- 17 August 2026
- Language
- EN