Mechanical systems with singular equilibria and the Coulomb dynamics of three charges - Skrypnik, W. I. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We consider mechanical systems for which the matrices of second partial derivatives of the potential energies at equilibriahave zero eigenvalues. It is assumed that their potential energies are holomorphic functions in these singular equilibriumstates. For these systems, we prove the existence of proper bounded (for positive time) solutions of the Newton equationof motion convergent to the equilibria in the infinite-time limit. These results are applied to the Coulomb systems of threepoint charges with singular equilibrium in a line.