Resonances and the stability of stationary points

  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

Book:
Advances in the Astronautical Sciences

ISBN: 978-087703565-7

Year of publication: 2011

Volume: 139

Pages: 3-19

Type: Book chapter

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Abstract

The question of Lyapunov stability of stationary points around a central body has been studied in 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 paper we deal with these resonances and apply appropriate results to establish the stability properties of the stationary points.

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Funding information

Supported by the Spanish Ministry of Science and Technology (Projects # MTM 2008-03818 and # AYA2008-05572).

Funders

  • Spanish Ministry of Science and Technology
    • MTM 2008-03818
    • AYA2008-05572