NDLI: Stress Matrices and Global Rigidity of Frameworks on Surfaces

Content Provider	Springer Nature Link
Author	Jackson, Bill Nixon, Anthony
Copyright Year	2015
Abstract	In 2005, Bob Connelly showed that a generic framework in $${\mathbb {R}}^d$$ is globally rigid if it has a stress matrix of maximum possible rank, and that this sufficient condition for generic global rigidity is preserved by the 1-extension operation. His results gave a key step in the characterisation of generic global rigidity in the plane. We extend these results to frameworks on surfaces in $${\mathbb {R}}^3$$ . For a framework on a family of concentric cylinders, cones or ellipsoids, we show that there is a natural surface stress matrix arising from assigning edge and vertex weights to the framework, in equilibrium at each vertex. In the case of cylinders and ellipsoids, we show that having a maximum-rank stress matrix is sufficient to guarantee generic global rigidity on the surface. We then show that this sufficient condition for generic global rigidity is preserved under 1-extension and use this to make progress on the problem of characterising generic global rigidity on the cylinder.
Ending Page	609
Page Count	24
Starting Page	586
File Format	PDF
ISSN	01795376
e-ISSN	14320444
Journal	Discrete & Computational Geometry
Issue Number	3
Volume Number	54
Language	English
Publisher	Springer US
Publisher Date	2015-08-20
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Planar graphs; geometric and topological aspects of graph theory Computational Mathematics and Numerical Analysis Rigidity and flexibility of structures Surfaces in Euclidean space Stress matrix Rigidity Global rigidity Combinatorics Framework on a surface
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Necessary Conditions for the Generic Global Rigidity of Frameworks on Surfaces

Symmetry-forced rigidity of frameworks on surfaces

Global rigidity of 2-dimensional linearly constrained frameworks

Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

Rigidity of Frameworks Supported on Surfaces

Rigidity of Frameworks Supported on Surfaces

A Characterization of Generically Rigid Frameworks on Surfaces of Revolution

Rigidity of linearly-constrained frameworks

A characterisation of generically rigid frameworks on surfaces of revolution

Stress Matrices and Global Rigidity of Frameworks on Surfaces

Similar Documents

Necessary Conditions for the Generic Global Rigidity of Frameworks on Surfaces

Symmetry-forced rigidity of frameworks on surfaces

Global rigidity of 2-dimensional linearly constrained frameworks

Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

Rigidity of Frameworks Supported on Surfaces

Rigidity of Frameworks Supported on Surfaces

A Characterization of Generically Rigid Frameworks on Surfaces of Revolution

Rigidity of linearly-constrained frameworks

A characterisation of generically rigid frameworks on surfaces of revolution

Stress Matrices and Global Rigidity of Frameworks on Surfaces