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

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

Nov 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..90..355s&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 90, Issue 3-4, pp. 355-360

Astronomy and Astrophysics

Astronomy

4

N-Body Problem, Central Configuration, Relative Equilibrium, Bifurcation, Rosette Configuration

Scientific paper

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 =m 0/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 ≥ μ c , and one when μ ≥ μ c . 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.

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