Resonances and the stability of stationary points around a central body

  1. Elipe, A. 2
  2. Lanchares, V. 1
  3. Pascual, A.I. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Journal:
Journal of the Astronautical Sciences

ISSN: 0021-9142

Year of publication: 2012

Volume: 59

Issue: 1-2

Pages: 5-20

Type: Article

SCOPUS: 2-s2.0-84901231719 WoS: WOS:000209125300003 GOOGLE SCHOLAR

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Abstract

The question of Lyapunov stability of stationaiy points around a central body has been studied in the absence of resonances and in the case of resonances of order 3 and 4, by means of the computation of the normal form up to second order. However, some special degenerate cases are not covered, as it happens for resonances of order 5 and 6, when the free parameters of the problem are chosen properly. In this article, we deal with these resonances and apply appropriate results to establish the stability properties of the stationary points.