Mechanical systems with singular equilibria and the Coulomb dynamics of three charges

• Date: 2018
• Main Authors: Skrypnik, W. I., Скрипник, В. І.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1573
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider mechanical systems for which the matrices of second partial derivatives of the potential energies at equilibria have zero eigenvalues. It is assumed that their potential energies are holomorphic functions in these singular equilibrium states. For these systems, we prove the existence of...