A variational approach to frozen planet orbits in helium

2021/03/29 by Kai Cieliebak, Cieliebak, Kai, Urs Frauenfelder +3 · 2 citations
Engineering · Physics and Astronomy · #47J30 #Astro and Planetary Science #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nuclear physics research studies #Spacecraft Dynamics and Control

paper · doi:10.48550/arxiv.2103.15485

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present variational characterizations of frozen planet orbits for the helium atom in the Lagrangian and the Hamiltonian picture. They are based on a Levi-Civita regularization with different time reparametrizations for the two electrons and lead to nonlocal functionals. Within this variational setup, we deform the helium problem to one where the two electrons interact only by their mean values and use this to deduce the existence of frozen planet orbits.

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• Loop space blow-up and scale calculus
• Spatial Stark-Zeeman Systems and Their Regularizations

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