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Central configurations of the five-body problem with two isosceles triangles

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Abstract

We present a complete classification of the central configurations of the 5-body problem in a plane having the following properties: three bodies, denoted by 1, 2, 3, are at the vertices of an isosceles triangle, and the other two bodies are symmetrically located with respect to the mediatrix of the segment joining the bodies 1 and 2.

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Acknowledgements

The first author is partially supported by Fundação de Amparo à Pesquisa do Estado de Minas Gerais [Grant Number APQ-03149-18] and by Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant Number 433285/2018-4]. The third author is partially supported by Fundação de Amparo à Pesquisa do Estado de Minas Gerais [Grant Numbers APQ-01158-17 and APQ-01105-18] and by Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant Number 311921/2020-5]. The fourth author was partially supported by CFisUC projects (UIDB/04564/2020 and UIDP/04564/2020), and ENGAGE SKA (POCI-01- 0145-FEDER-022217), funded by COMPETE 2020 and FCT, Portugal.

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Authors and Affiliations

  1. Instituto de Matemática e Computação, Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, Itajubá, MG, CEP 37.500-903, Brazil

    Antonio Carlos Fernandes, Braulio Augusto Garcia, Luis Fernando Mello & Lucas Ruiz dos Santos

  2. CFisUC, Department of Physics, University of Coimbra, Coimbra, Portugal

    Lucas Ruiz dos Santos

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  1. Antonio Carlos Fernandes
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  2. Braulio Augusto Garcia
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  3. Luis Fernando Mello
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  4. Lucas Ruiz dos Santos
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Correspondence to Antonio Carlos Fernandes.

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Fernandes, A.C., Garcia, B.A., Mello, L.F. et al. Central configurations of the five-body problem with two isosceles triangles. Z. Angew. Math. Phys. 72, 156 (2021). https://doi.org/10.1007/s00033-021-01585-9

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  • DOI: https://doi.org/10.1007/s00033-021-01585-9

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