2024/10/06 by Yuwei Ou, Ou, Yuwei, Алессандро Порталури +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #53D12 #70F10 #70F16 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2410.04374
openalex publication_date 2024/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the gravitation n-body Problem, a homothetic orbit is a special solution of the Newton's Equations of motion, in which each body moves along a straight line through the center of mass and forming at any time a central configuration. In 2020, Portaluri et al. proved that under a spectral gap condition on the limiting central configuration, known in literature as non-spiraling or [BS]-condition, the Morse index of an asymptotic colliding motion is finite. Later Ou et al. proved this result for other classes of unbounded motions, e.g. doubly asymptotic motions (e.g. doubly homothetic motions). In this paper we prove that for a homothetic motion, irrespective of how large the index of the limiting central configuration and how large the energy level is, the following alternative holds: if the non-spiraling condition holds then the Morse index is 0 otherwise it is infinite.