NDLI: Symmetry as a Sufficient Condition for a Finite Flex

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Schulze, Bernd
Copyright Year	2010
Abstract	We show that if the joints of a bar and joint framework $(G,p)$ are positioned as generically as possible subject to given symmetry constraints and $(G,p)$ possesses a fully symmetric infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their 1978 paper The Rigidity of Graphs [Trans. Amer. Math. Soc., 245 (1978), pp. 279289] and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous nonsymmetric methods.
Starting Page	1291
Ending Page	1312
Page Count	22
File Format	PDF
ISSN	08954801
DOI	10.1137/090776238
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-10-05
Access Restriction	Subscribed
Subject Keyword	bar and joint frameworks rigid and flexible frameworks Applications of group representations to physics Rigidity and flexibility of structures mechanism symmetric frameworks infinitesimal motion finite motion
Content Type	Text
Resource Type	Article
Subject	Mathematics

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

Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks

Symmetry as a sufficient condition for a finite flex

Crystal frameworks, symmetry and affinely periodic flexes.

The Orbit Rigidity Matrix of a Symmetric Framework

A necessary condition for generic rigidity of bar-and-joint frameworks in $d$-space

Infinitesimal rigidity of symmetric bar-joint frameworks (2014)

Maxwell-Laman counts for bar-joint frameworks in normed spaces

Infinitesimal rigidity for non-Euclidean bar-joint frameworks

States of self-stress in symmetric frameworks and applications

Symmetry as a Sufficient Condition for a Finite Flex

Similar Documents

Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks

Symmetry as a sufficient condition for a finite flex

Crystal frameworks, symmetry and affinely periodic flexes.

The Orbit Rigidity Matrix of a Symmetric Framework

A necessary condition for generic rigidity of bar-and-joint frameworks in $d$-space

Infinitesimal rigidity of symmetric bar-joint frameworks (2014)

Maxwell-Laman counts for bar-joint frameworks in normed spaces

Infinitesimal rigidity for non-Euclidean bar-joint frameworks

States of self-stress in symmetric frameworks and applications

Symmetry as a Sufficient Condition for a Finite Flex