Celestial Mechanics and Dynamical Astronomy

, Volume 90, Issue 3, pp 355–360

Bifurcation of central configuration in the 2N+1 body problem

Article

DOI: 10.1007/s10569-004-1991-2

Cite this article as:
Sekiguchi, M. Celestial Mech Dyn Astr (2004) 90: 355. doi:10.1007/s10569-004-1991-2

Abstract

The bifurcation of central configuration in the Newtonian N-body problem for any odd number N ≥ 7 is shown. We study a special case where 2n particles of mass m on the vertices of two different coplanar and concentric regular n-gons (rosette configuration) and an additional particle of mass m0 at the center are governed by the gravitational law he 2n+1 body problem. This system is of two degrees of freedom and permits only one mass parameter μ =m0/m. This parameter μ controls the bifurcation. If n≥ 3, namely any odd N ≥ 7, then the number of central configurations is three when μ ≥ μc, and one when μ ≥ μc. By combining the results of the preceding studies and our main theorem, explicit examples of bifurcating central configuration are obtained for N ≤ 13, for any odd N ∈ [15,943], and for any N ≥ 945.

Keywords

N-body problem central configuration relative equilibrium bifurcation rosette configuration 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Kisarazu National College of TechnologyChibaJapan

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