Resonant motion in the restricted three-body problem
type: Item
instance of: scholarly article
title: Resonant motion in the restricted three-body problem
zbMATH Open document ID: 0780.70004
DOI: 10.1007/BF00699733
author: John D. Hadjidemetriou
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1994-02-06T00:00:00Z
review text: The resonant structure of the restricted three-body problem for the Sun- Jupiter asteroid system in the plane is studied, both for a circular and an elliptic orbit of Jupiter. Three typical resonances are studied, the 2:1, 3:1 and 4:1 mean motion resonance of the asteroid with Jupiter. In each case we start with the unperturbed two-body system ``Sun-asteroid'', and we study the continuation of the periodic orbits when the perturbation due to a circular orbit of Jupiter is introduced. Families of periodic orbits of the first and of the second kind are presented. The structure of the phase space on a surface of section is also given. Next, we study the families of periodic orbits of the asteroid in the elliptic restricted problem with the eccentricity of Jupiter as a parameter.
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 429323
zbMATH Keywords: Sun-Jupiter asteroid system
zbMATH Keywords: periodic orbits
zbMATH Keywords: phase space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00699733
OpenAlex ID: W4246105466
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description: scientific article; zbMATH DE number 429323