Central Configurations of the Symmetric Restricted 4-Body Problem

Details Central Configurations of the Symmetric Restricted 4-Body Problem Central Configurations of the Symmetric Restricted 4-Body Problem

Dec 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003cemda..87..371a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 87, Issue 4, p. 371-381 (2003).

Astronomy and Astrophysics

Astronomy

Scientific paper

We consider the symmetric planar (3 + 1)-body problem with finite masses m1 = m2 = 1, m3 = µ and one small mass m4 = ɛ. We count the number of central configurations of the restricted case ɛ = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with μ as the parameter. The diagram shows a folding bifurcation at a value consistent with that found numerically by Meyer [9] and it is shown that for small ɛ > 0 the bifurcation diagram persists, thus leading to an exact count of central configurations and a folding bifurcation for small m4 > 0.

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