Coulomb Control of Polygonal Linkages

Giorgi N. Khimshiashvili; Gaiane Yu Panina; Dirk Siersma

doi:10.1007/s10883-014-9218-7

Coulomb Control of Polygonal Linkages

Giorgi N. Khimshiashvili, Gaiane Yu Panina, Dirk Siersma

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of Coulomb potential for appropriate values of charges of vertices. Similar problems are treated for the equilateral pentagonal linkage. Some corollaries and applications in the spirit of control theory are also presented.

Original language	English
Pages (from-to)	491-501
Journal	Journal of Dynamical and Control Systems
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s10883-014-9218-7
Publication status	Published - 17 Mar 2014

Keywords

Coulomb potential
Critical point
Equilibrium
Planar configuration
Point charge
Polygonal linkage

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10.1007/s10883-014-9218-7

https://arxiv.org/pdf/1304.6214.pdf

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abstract = "Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of Coulomb potential for appropriate values of charges of vertices. Similar problems are treated for the equilateral pentagonal linkage. Some corollaries and applications in the spirit of control theory are also presented.",

keywords = "Coulomb potential, Critical point, Equilibrium, Planar configuration, Point charge, Polygonal linkage",

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AU - Khimshiashvili, Giorgi N.

AU - Panina, Gaiane Yu

AU - Siersma, Dirk

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Y1 - 2014/3/17

N2 - Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of Coulomb potential for appropriate values of charges of vertices. Similar problems are treated for the equilateral pentagonal linkage. Some corollaries and applications in the spirit of control theory are also presented.

AB - Equilibria of polygonal linkage with respect to Coulomb potential of point charges placed at the vertices of linkage are considered. It is proved that any convex configuration of a quadrilateral linkage is the point of global minimum of Coulomb potential for appropriate values of charges of vertices. Similar problems are treated for the equilateral pentagonal linkage. Some corollaries and applications in the spirit of control theory are also presented.

KW - Coulomb potential

KW - Critical point

KW - Equilibrium

KW - Planar configuration

KW - Point charge

KW - Polygonal linkage

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DO - 10.1007/s10883-014-9218-7

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SP - 491

EP - 501

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 4

ER -

Coulomb Control of Polygonal Linkages

Abstract

Keywords

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