Point Charges and Polygonal Linkages
Metric Geometry
2018-01-12 v2 Optimization and Control
Abstract
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.
Cite
@article{arxiv.1503.04463,
title = {Point Charges and Polygonal Linkages},
author = {Giorgi Khimshiashvili and Gaiane Panina and Dirk Siersma and Vladimir Zolotov},
journal= {arXiv preprint arXiv:1503.04463},
year = {2018}
}