Stability of the triangular Lagrange points beyond Gascheau's value

B. Sicardy (1)

1 OBSPM - Observatoire de Paris - Site de Meudon

We examine the stability of the triangular Lagrange points and for secondary masses larger than the Gascheau's value (also known as the Routh value) in the restricted, planar circular three-body problem. Above that limit the triangular Lagrange points are linearly unstable. Here we show that between  and , the and points are globally stable in the sense that a particle released at those points at zero velocity (in the corotating frame) remains in the vicinity of those points for an indefinite time. We also show that there exists a family of stable periodic orbits surrounding or for . We show that  is actually the first value of a series corresponding to successive period doublings of the orbits, which exhibit cycles around or . Those orbits follow a Feigenbaum cascade leading to disappearance into chaos at a value which generalizes Gascheau's work.

Mots clés: Three-body problem; Lagrange points; Global stability; Routh's critical mass ratio; Feigenbaum cascade

B. Sicardy. Stability of the triangular Lagrange points beyond Gascheau's value. Celestial Mechanics and Dynamical Astronomy, 2010, 107 (1-2), pp.145-155. ⟨10.1007/s10569-010-9259-5⟩. ⟨hal-00552502⟩