We study the critical points of Coulomb energy considered as a function on configuration
spaces associated with certain geometric constraints. Two settings of such kind are …

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 curve …

The isolation and nondegeneracy of constrained extrema arising in geometric problems and
mathematical models of electrostatics are studied. In particular, it is proved that a convex …

We show that the incenter of an isosceles triangle is a stable equilibrium point of the
electrostatic potential of certain point charges placed at its vertices. To this end, explicit …

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 …

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 …

We discuss various aspects of a general problem naturally arising in the framework of an
approach to inverse problems of electrostatics. In particular, we describe some …

For a polygonal linkage, we produce a fast navigation algorithm on its configuration space.
The basic idea is to approximate M (L) by the vertex-edge graph of the cell decomposition of …

We discuss equilibrium configurations of Coulomb potential of point charges in convex
domains of the plane and three-dimensional Euclidean space. For a triple of points, we give …

Изучается вопрос об изолированности и невырожденности условных экстремумов,
возникающих в некоторых геометрических задачах и математических моделях …