Asymptotic velocity for four celestial bodies

Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree...

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Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2018-10, Vol.376 (2131), p.20170426
Main Author: Knauf, Andreas
Format: Article
Language:English
Subjects:
Asymptotic Velocity
Celestial Mechanics
Scattering Theory
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description Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree −α for α∈(0, 2), that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and almost all initial conditions on the energy surface. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.
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source JSTOR Archival Journals and Primary Sources Collection; Royal Society Publishing Jisc Collections Royal Society Journals Read & Publish Transitional Agreement 2025 (reading list)
subjects Asymptotic Velocity
Celestial Mechanics
Scattering Theory
title Asymptotic velocity for four celestial bodies
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