Structural rigidity. II: Almost infinitesimally rigid bar frameworks
[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.
scientific article; zbMATH DE number 3931068