A remarkable periodic solution of the three-body problem in the case of equal masses

• Autores: Alain Chenciner, Richard Montgomery
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 152, Nº 3, 2000, págs. 881-901
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ¿Lagrange relative equilibrium¿ in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle.