6 citations · 12 across the 6 of their papers we have counts for
8 papers
Complex invariants of poristic Steiner 4-chains
Ana Diakvnishvili, Giorgi Khimshiashvili
We are concerned with the Steiner chains consisting of four circles. More precisely, we deal with the so-called complex moments of Steiner 4-chains introduced in a recent paper by…
Hooke and Coulomn Energy of Tripod Spiders
Giorgi Khimshiashvili, Dirk Siersma
Tripod spiders are the simplest examples of arachnoid mechanisms. Their workspaces and configuration spaces are well known. For Hooke potential, we give a complete description of t…
Area-perimeter duality in polygon spaces
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail…
Extremal areas of polygons with fixed perimeter
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
We consider the configuration space of planar -gons with fixed perimeter, which is diffeomorphic to the complex projective space . The oriented area function…
Point Charges and Polygonal Linkages
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma +1
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 charge…
Equilibria of point charges on convex curves
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
We study the equilibrium positions of three points on a convex curve under influence of the Coulomb potential. We identify these positions as orthotripods, three points on the curv…
Cross Ratios of Quadrilateral Linkages
Giorgi Khimshiashvili, Dirk Siersma
We discuss the cross-ratio map of planar quadrilateral linkages, also in the case when one of the links is telescopic. Most of our results are valid for a planar quadrilateral link…
Coulomb control of polygonal linkages
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
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…