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Rosette Central Configurations, Degenerate Central Configurations and Bifurcations

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Abstract

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian n-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where n particles of mass m 1 lie at the vertices of a regular n-gon, n particles of mass m 2 lie at the vertices of another n-gon concentric with the first, but rotated of an angle π /n, and an additional particle of mass m 0 lies at the center of mass of the system. This system admits two mass parameters μ  =  m 0/m 1 and ε  =  m 2/m 1. We show that, as μ varies, if n >  3, there is a degenerate central configuration and a bifurcation for every ε  >  0, while if n = 3 there is a bifurcation only for some values of ε.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, CA, 92697, U.S.A.

    J. Lei & M. Santoprete

  2. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China

    J. Lei

Authors
  1. J. Lei
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  2. M. Santoprete
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Correspondence to M. Santoprete.

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Lei, J., Santoprete, M. Rosette Central Configurations, Degenerate Central Configurations and Bifurcations. Celestial Mech Dyn Astr 94, 271–287 (2006). https://doi.org/10.1007/s10569-005-5534-2

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  • DOI: https://doi.org/10.1007/s10569-005-5534-2

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