HIGHER-ORDER RIGIDITY - WHAT IS THE PROPER DEFINITION

Authors
CONNELLY R SERVATIUS H
Citation
R. Connelly et H. Servatius, HIGHER-ORDER RIGIDITY - WHAT IS THE PROPER DEFINITION, Discrete & computational geometry, 11(2), 1994, pp. 193-200
Citations number
11
Categorie Soggetti
Computer Sciences, Special Topics","Mathematics, General","Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
11
Issue
2
Year of publication
1994
Pages
193 - 200
Database
ISI
SICI code
0179-5376(1994)11:2<193:HR-WIT>2.0.ZU;2-6
Abstract
We show that there is a bar-and-joint framework G(p) which has a confi guration p in the plane such that the component of p in the space of a ll planar configurations of G has a cusp at p. At the cusp point, the mechanism G(p) turns out to be third-order rigid in the sense that eve ry third-order flex must have a trivial first-order component. The exi stence of a third-order rigid framework that is not rigid calls into q uestion the whole notion of higher-order rigidity.