Periodic Rigidity on a Variable Torus Using Inductive Constructions
Keywords: periodic framework, generic rigidity, Henneberg operation
AbstractIn this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.