Structural rigidity. II: Almost infinitesimally rigid bar frameworks
type: Item
instance of: scholarly article
title: Structural rigidity. II: Almost infinitesimally rigid bar frameworks
zbMATH Open document ID: 0582.05054
DOI: 10.1016/0166-218X(86)90068-5
published in: Discrete Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: [For part I see the author's paper in Ann. Discrete Math. 8, 143-161 (1980; Zbl 0457.05065).] Structural rigidity of bar frameworks is studied in the case that the corresponding rigidity matrix has rank one less than the number of columns. This represents the case just next to infinitesimal rigidity and is likely to occur at the exceptional loci of generically inf-rigid frameworks. Applying a general rigidity criterion from the preceding paper we obtain necessary and sufficient rigidity conditions in which (i) vectors are assigned to binary trees, (ii) fixed linear combinations (whose coefficients are polynomials of several real variables) are formed and (iii) it is tested whether these combinations may simultaneously belong to a certain vector space. Although this criterion is too complex for theorem proving it may be easily applied in concrete situations.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 70J99
Mathematics Subject Classification ID: 15A99
Mathematics Subject Classification ID: 74G99
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 3931068
zbMATH Keywords: Structural rigidity
zbMATH Keywords: bar frameworks
Wikidata QID: Q56032213
author: Ivo G. Rosenberg
MaRDI profile type: Publication
cites work: The Rigidity of Graphs
cites work: The rigidity of graphs. II
cites work: The rigidity of certain cabled frameworks and the second-order rigidity of arbitrary triangulated convex surfaces
cites work: Addenda
cites work: Structural Rigidity I: Foundations and Rigidity Criteria
cites work: The Algebraic Geometry of Stresses in Frameworks
description: scientific article; zbMATH DE number 3931068