Newton Algorithm on Constraint Manifolds and the 5-electron Thomson problem

摘要

We give a description of numerical Newton algorithm on a constraint manifoldusing only the ambient coordinates (usually Euclidean coordinates) and thegeometry of the constraint manifold. We apply the numerical Newton algorithm ona sphere in order to find the critical configurations of the 5-electron Thomsonproblem. As a result, we find a new critical configuration of a regularpentagonal type. We also make an analytical study of the criticalconfigurations found previously and determine their nature using Morse-Botttheory. Last section contains an analytical study of critical configurationsfor Riesz s-energy of 5-electron on a sphere and their bifurcation behavior ispointed out.