Double-Distance Frameworks and Mixed Sparsity Graphs

Abstract

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a variety of such contexts. The main results are combinatorial characterisations for (i) frameworks restricted to surfaces with both Euclidean and geodesic distance constraints, (ii) frameworks in the plane with Euclidean and non-Euclidean distance constraints, and (iii) direction-length frameworks in the non-Euclidean plane.2010 Mathematics Subject Classification. 52C25, 05C10, 51E15

Non-Euclidean braced grids

“…For some further discussions of non-Euclidean frameworks see also Dewar [7], Kitson [9], Kitson, Nixon and Schulze [10], and Nixon and Power [14].…”

Non-Euclidean braced grids

“…For some further discussions of non-Euclidean frameworks see also Dewar [7], Kitson [9], Kitson, Nixon and Schulze [10], and Nixon and Power [14].…”