Hip-hop solutions of the 2N-body problem

  • Esther Barrabés
  • Josep Maria Cors
  • Conxita Pinyol
  • Jaume Soler
Original Article

Abstract

Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.

Keywords

N-body problem Analytic continuation Hip-hop Choreographies 

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Copyright information

© Springer Science+Business Media B.V 2006

Authors and Affiliations

  • Esther Barrabés
    • 1
  • Josep Maria Cors
    • 2
  • Conxita Pinyol
    • 3
  • Jaume Soler
    • 4
  1. 1.Departament d’Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain
  2. 2.Departament de Matemàtica Aplicada IIIUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Departament d’Economia i Història EconòmicaUniversitat Autònoma de BarcelonaBarcelonaSpain
  4. 4.Departament d’Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain

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