Geometry of Configuration Spaces of Tensegrities

Abstract  Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in ℝ
^d
to admit a nonzero self-stress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all n-tuples in ℝ
^d
. In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related
to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata
for tensegrities in the plane with a small number of vertices.

• Content Type Journal Article
• DOI 10.1007/s00454-009-9229-4
• Authors
  
  
  • Franck Doray, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
  • Oleg Karpenkov, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
  • Jan Schepers, Universiteit Leiden Mathematisch Instituut P.O. Box 9512 2300 RA Leiden The Netherlands
  
  

• Journal Discrete and Computational Geometry
• Online ISSN 1432-0444
• Print ISSN 0179-5376

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Original source : http://www.springerlink.com/content/k60vq2675l2217...