Rigidity of symmetric frameworks in normed spaces

Kitson, Derek; Nixon, Anthony; Schulze, Bernd

doi:10.1016/j.laa.2020.08.004

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Cited by 6 publications

(2 citation statements)

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

Section: 3mentioning

confidence: 99%

Non-Euclidean braced grids

Power¹

2020

Mathematical Proceedings of the Royal Irish Academy

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

Section: 3mentioning

confidence: 99%

Non-Euclidean braced grids

Power¹

2020

Mathematical Proceedings of the Royal Irish Academy

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

Section: 3mentioning

confidence: 99%

Non-Euclidean braced grids

Power¹

2020

Mathematical Proceedings of the Royal Irish Academy

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Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial part of the conditions is given in terms of a matroid for the bicoloured bipartite multigraph defined by the braces.Theorem 1.1. Let G(B) be an m × n braced grid bar-joint framework in R 2 and let • be a differentiable, strictly convex non-Euclidean norm. Then the following are equivalent.() and the bicoloured braces graph of G(B) is a spanning subgraph of K 2 m,n with an independent cycle in each path-connected component. A simple graph is a cycle-rooted tree if there is an edge whose removal gives a tree, and is a cycle-rooted forest if each connected components is a cycle-rooted tree. We extend this tree and forest terminology to bicoloured multigraphs G whose monochrome subgraphs are simple. Thus G is a cycle-rooted tree if there is an edge whose removal gives a tree. The graph condition in (ii) means that the braces graph contains a spanning subgraph that is an independent cycle-rooted 2000 Mathematics Subject Classification.

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