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Some analytical results about periodic orbits in the restricted three body problem with dissipation

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Abstract

We present some analytical results about the existence of periodic orbits for the planar restricted three body problem with dissipation considered recently by Celletti et al. (CMDA 109, 265, 2011) We show that, under fairly general conditions on the dissipation term, the circular orbits cannot be continued to the dissipative framework. Moreover, we give general conditions for the occurrence or not of a Hopf bifurcation around the libration points L 4 and L 5. Our results are consistent with the numerical findings of Celletti et al.

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Authors and Affiliations

  1. Fac. Ciências da Univ. de Lisboa e Centro de Matemática e Aplicações Fundamentais, Campo Grande, Edifício C6, piso 2, 1749-016, Lisboa, Portugal

    Alessandro Margheri & Carlota Rebelo

  2. Departamento de Matemática Aplicada, Universidad de Granada, 18071, Granada, Spain

    Rafael Ortega

Authors
  1. Alessandro Margheri
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  2. Rafael Ortega
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  3. Carlota Rebelo
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Correspondence to Alessandro Margheri.

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Margheri, A., Ortega, R. & Rebelo, C. Some analytical results about periodic orbits in the restricted three body problem with dissipation. Celest Mech Dyn Astr 113, 279–290 (2012). https://doi.org/10.1007/s10569-012-9415-1

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  • DOI: https://doi.org/10.1007/s10569-012-9415-1

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