Local and Infinitesimal Rigidities

Abdo Y. Alfakih
Additional contact information
Abdo Y. Alfakih: University of Windsor, Department of Mathematics and Statistics

Chapter Chapter 9 in Euclidean Distance Matrices and Their Applications in Rigidity Theory, 2018, pp 185-210 from Springer

Abstract: Abstract This chapter focuses on the problems of local rigidity and infinitesimal rigidity of bar frameworks. These problems have a long and rich history going back at least as far as Cauchy [51]. The main tools in tackling these problems are the rigidity matrix R and the dual rigidity matrix R ̄ $$\bar{R}$$ . While R is defined in terms of the underlying graph G and configuration p, R ̄ $$\bar{R}$$ is defined in terms of the complement graph Ḡ $$\bar{G}$$ and Gale matrix Z. Gale matrix Nonetheless, both matrices R and R ̄ $$\bar{R}$$ carry the same information. The chapter concludes with a discussion of generic local rigidity in dimension 2, where the local rigidity problem reduces to a purely combinatorial one depending only on graph G. The literature on the theory of local and infinitesimal rigidities is vast [59, 57, 66, 97, 194]. However, in this chapter, we confine ourselves to discussing only the basic results and the results pertaining to EDMs.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-97846-8_9

Ordering information: This item can be ordered from
http://www.springer.com/9783319978468

DOI: 10.1007/978-3-319-97846-8_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().