Abstract
The problem analyzed is the classical non-regularized Hamiltonian formulation of a restricted three body problem under the influence of Coulomb-interactions. Completing the large literature on Helium-like systems we will consider the motions around a fixed positive point charge of (i) one negative and one positive point charge as well as the “classical” issue of (ii) two negative point charges. Thereby, all our considerations deal with arbitrary positive and negative charge values of the mass particles. Here, we give necessary and sufficient conditions for the existence of genuine equilibria in such systems—recall that there are none in the usual classical Helium-atom—and analyze their linearized stability. The thus obtained insights allow us to study the dynamics near such genuine equilibria.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
