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 language | English |
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Pages (from-to) | 519-529 |
Number of pages | 11 |
Journal | Central European Journal of Mathematics |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Wiskunde en Informatica (WIIN)
- Mathematics
- Landbouwwetenschappen
- Natuurwetenschappen
- Wiskunde: algemeen