An analytic estimation for the instability interval near second order resonances in the restricted three-body problem

Jaume Llibre; Jaume Soler

doi:https://doi.org/10.1007/BF00952087

An analytic estimation for the instability interval near second order resonances in the restricted three-body problem

Jaume Llibre, Jaume Soler

Department of Mathematics

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Abstract

Periodic orbits of the first kind of the planar circular restricted three-body problem are linearly stable except in the neighbourhood of second order resonances, where an interval of unstable orbits appears when the mass parameter is not zero. Our main result is the estimation of the length of the instability interval. © 1994 Birkhäuser Verlag.

Original language	English
Pages (from-to)	956-977
Journal	ZAMP Zeitschrift für angewandte Mathematik und Physik
Volume	45
DOIs	https://doi.org/10.1007/BF00952087
Publication status	Published - 1 Nov 1994

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@article{679a76d3ac9841608497f1f1d295262f,

title = "An analytic estimation for the instability interval near second order resonances in the restricted three-body problem",

abstract = "Periodic orbits of the first kind of the planar circular restricted three-body problem are linearly stable except in the neighbourhood of second order resonances, where an interval of unstable orbits appears when the mass parameter is not zero. Our main result is the estimation of the length of the instability interval. {\textcopyright} 1994 Birkh{\"a}user Verlag.",

author = "Jaume Llibre and Jaume Soler",

year = "1994",

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doi = "https://doi.org/10.1007/BF00952087",

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journal = "Zeitschrift fur Angewandte Mathematik und Physik",

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publisher = "Birkhauser Verlag Basel",

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TY - JOUR

T1 - An analytic estimation for the instability interval near second order resonances in the restricted three-body problem

AU - Llibre, Jaume

AU - Soler, Jaume

PY - 1994/11/1

Y1 - 1994/11/1

N2 - Periodic orbits of the first kind of the planar circular restricted three-body problem are linearly stable except in the neighbourhood of second order resonances, where an interval of unstable orbits appears when the mass parameter is not zero. Our main result is the estimation of the length of the instability interval. © 1994 Birkhäuser Verlag.

AB - Periodic orbits of the first kind of the planar circular restricted three-body problem are linearly stable except in the neighbourhood of second order resonances, where an interval of unstable orbits appears when the mass parameter is not zero. Our main result is the estimation of the length of the instability interval. © 1994 Birkhäuser Verlag.

U2 - https://doi.org/10.1007/BF00952087

DO - https://doi.org/10.1007/BF00952087

M3 - Article

SN - 0044-2275

VL - 45

SP - 956

EP - 977

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

ER -

An analytic estimation for the instability interval near second order resonances in the restricted three-body problem

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