Coulomb control of polygonal linkages
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
TL;DR
This paper investigates how Coulomb potentials influence the equilibrium configurations of polygonal linkages, demonstrating that convex quadrilaterals and certain pentagons can be stabilized as global minima through charge adjustments, with implications for control theory.
Contribution
It introduces a novel approach to controlling polygonal linkages by manipulating Coulomb charges to achieve desired equilibrium configurations.
Findings
Convex quadrilaterals can be stabilized as Coulomb potential minima.
Similar stabilization results are extended to equilateral pentagons.
Applications in control theory are discussed.
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.
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Taxonomy
TopicsSpace Satellite Systems and Control · Dynamics and Control of Mechanical Systems · Robotic Path Planning Algorithms