Qualitative Theory of Dynamical Systems

, Volume 12, Issue 2, pp 293–303 | Cite as

On Stacked Planar Central Configurations with Five Bodies when One Body is Removed

Article

Abstract

In this paper we answer the following question posed by Hampton (Nonlinearity 18:2299–2304, 2005). In addition to symmetric collinear configurations and the square with a mass at its center are there any planar five-body central configurations with a subset forming a four-body central configuration? We prove that, for non-collinear configurations, the only possible strictly planar central configuration for the five-body problem for which it can be removed one body such that the remaining four bodies are already in a central configuration is obtained with four bodies of equal masses at the vertices of a square and the fifth body of arbitrary mass at the center of the square.

Keywords

Planar central configuration Stacked central configuration Five-body problem Four-body problem 

Mathematics Subject Classification (2000)

Primary 70F10 70F15 Secondary 37N05 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Antonio Carlos Fernandes
    • 1
  • Luis Fernando Mello
    • 1
  1. 1.Instituto de Ciências ExatasUniversidade Federal de ItajubáItajubáBrazil

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