Point Charges and Polygonal Linkages

We investigate the critical points of Coulomb potential of point charges placed at the vertices of a planar polygonal linkage. It is shown that, for a collection of positive charges on a pentagonal linkage, there is a unique critical point in the set of convex configurations which is the point of ab...

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Bibliographic Details
Published in:arXiv.org 2015-05
Main Authors: Giorgi Khimshiashvili, Panina, Gaiane, Siersma, Dirk, Zolotov, Vladimir
Format: Article
Language:English
Subjects:
Apexes
Configurations
Coulomb potential
Critical point
Online Access:Get full text
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Summary:We investigate the critical points of Coulomb potential of point charges placed at the vertices of a planar polygonal linkage. It is shown that, for a collection of positive charges on a pentagonal linkage, there is a unique critical point in the set of convex configurations which is the point of absolute minimum. This enables us to prove that two controlling charges are sufficient to navigate between any two convex configurations of a pentagonal linkage.
ISSN:2331-8422
DOI:10.48550/arxiv.1503.04463