School of Mathematical Sciences

Rigidity of linearly constrained frameworks menu

Rigidity of linearly constrained frameworks

Speaker: 
Hakan Guler (QMUL)
Date/Time: 
Fri, 03/11/2017 - 16:00
Room: 
W316, Queen's Building
Seminar series: 

A linearly constrained framework in d-dimensions is a d-dimensional bar-and-joint framework such that each vertex is allowed to move on a specific hyperplane. We denote linearly constrained frameworks by a triple (G, p, q) where G = (V, E) is a graph, p : V → R^d is the realisation map for the vertices, and q : V → R^d is the map that assigns unit vectors to the vertices that are normal to the associated hyperplanes. A linearly constrained framework is rigid if the only continuous motion of the vertices which satisfies the hyperplane constraints for the vertices and the length constraints for the edges, is the trivial motion which keeps each vertex fixed. We say that (G, p, q) is generic if (p, q) is algebraicly independent over the rationals. Streinu and Theran characterised generic rigidity of linearly constrained frameworks in R^2. In this talk we will give a characterisation for generic rigidity of linearly constrained frameworks in R^3. This is joint work with Bill Jackson.