Critical configurations of planar robot arms

G. Khimshiashvili, G. Panina, D. Siersma, A. Zhukova

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, P can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints and derive a formula for the Morse index of a critical configuration.
Original languageEnglish
Pages (from-to)519-529
Number of pages11
JournalCentral European Journal of Mathematics
Volume11
Issue number3
DOIs
Publication statusPublished - 2013

Keywords

  • Wiskunde en Informatica (WIIN)
  • Mathematics
  • Landbouwwetenschappen
  • Natuurwetenschappen
  • Wiskunde: algemeen

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