Coulomb Control of Polygonal Linkages
- 142 Downloads
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.
KeywordsPolygonal linkage Planar configuration Point charge Coulomb potential Critical point Equilibrium
- 1.Connelly R., Demaine E. Geometry and topology of plygonal linkages, Handbook of discrete and computational geometry, 2nd ed. Boca Raton: CRC Press; 2004, pp. 197–218.Google Scholar
- 4.Khimshiashvili G., Panina G. Cyclic polygons are critical points of area. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 2008;360(8):238–245.Google Scholar
- 5.Khimshiashvili G., Siersma D. Cyclic configurations of planar multiple penduli. ICTP Preprint IC/2009/047. p. 11.Google Scholar
- 8.Maxwell J.C. A treatise on electricity and magnetism: London; 1853.Google Scholar
- 9.Panina G. Moduli space of a planar polygonal linkage: a combinatorial description. arXiv:1209.3241.