Necessary Conditions for the Generic Global Rigidity of Frameworks on Surfaces

Autor:	Jackson, Bill, McCourt, Thomas, Nixon, Anthony
Rok vydání:	2013
Předmět:	Mathematics - Metric Geometry Mathematics - Combinatorics 52C25
Druh dokumentu:	Working Paper
Popis:	A result due in its various parts to Hendrickson, Connelly, and Jackson and Jord\'an, provides a purely combinatorial characterisation of global rigidity for generic bar-joint frameworks in $\mathbb{R}^2$. The analogous conditions are known to be insufficient to characterise generic global rigidity in higher dimensions. Recently Laman-type characterisations of rigidity have been obtained for generic frameworks in $\mathbb{R}^3$ when the vertices are constrained to lie on various surfaces, such as the cylinder and the cone. In this paper we obtain analogues of Hendrickson's necessary conditions for the global rigidity of generic frameworks on the cylinder, cone and ellipsoid. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1306.2346 Zobrazit plný text záznamu View this record from Arxiv