title: Critical configurations of planar robot arms
metadata.name: dc.contributor.author
metadata.value: Khimshiashvili, G.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Panina, G.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Siersma, D.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhukova, A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2015-08-28T05:30:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2015-08-28T05:30:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2013-03
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1715
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Springer
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Central European Journal of Mathematics;Volume 11, Issue 3
metadata.lang: -
metadata.name: dc.title
metadata.value: Critical configurations of planar robot arms
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 1201.5447.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1715/1/1201.5447.pdf
resources.format: Adobe PDF
resources.description: Arxiv preprint
resources.size: 526,19 kB