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Regular and Chaotic Dynamics

, Volume 23, Issue 7–8, pp 961–973 | Cite as

On the Sectional Curvature Along Central Configurations

  • Connor JackmanEmail author
  • Josué Meléndez
Article
  • 4 Downloads

Abstract

In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi–Maupertuis metric. This characterization works for the N-body problem with general masses and any 1/rα potential with α > 0. We also obtain dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces (α ≥ 2).

Keywords

instability homographic solutions central configurations Jacobi–Maupertuis metric 

MSC2010 numbers

70F10 37N05 70G45 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.UC Santa CruzSanta CruzUSA
  2. 2.UAM–Iztapalapa San Rafael Atlixco 186Código PostalMéxico

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