Stability and bifurcations of the figure-8 solution of the three-body problem.
The stability properties of a recently discovered solution of the general three-body problem with equal masses and the shape of a figure 8 are analyzed as the masses are varied. It is shown by numerical continuation and the evaluation of the characteristic multipliers that the solution is stable only in a narrow mass interval. Other less symmetrical and unstable solutions with equal masses in the same homotopy class as the figure-8 orbit have been found. The branching behavior is also analyzed.
Galán
J
J
Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain. jgv@ma2.us.es
Muñoz-Almaraz
F J
FJ
Freire
E
E
Doedel
E
E
Vanderbauwhede
A
A