Related Experiment Videos
Stability and bifurcations of the figure-8 solution of the three-body problem
J Galán1, F J Muñoz-Almaraz, E Freire
1Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, University of Seville, Camino de los Descubrimientos s/n, 41092 Seville, Spain. jgv@ma2.us.es
Physical Review Letters
|June 13, 2002
Abstract:
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.