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Sicardy Bruno

Stability of the triangular Lagrange points beyond Gascheau's value

Celestial Mechanics and Dynamical Astronomy, 2010, vol. 107, pp. 145-155

Référence DOI : 10.1007/s10569-010-9259-5
Référence ADS : 2010CeMDA.107..145S

Résumé :

We examine the stability of the triangular Lagrange points L <SUB>4</SUB> and L <SUB>5</SUB> for secondary masses larger than the Gascheau's value {mu_G= (1-sqrt{23/27}/2)= 0.0385208ldots} (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 mu <SUB> G </SUB> and {mu &ap; 0.039}, the L <SUB>4</SUB> and L <SUB>5</SUB> 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 L <SUB>4</SUB> or L <SUB>5</SUB> for {mu ge mu_G}. We show that mu <SUB> G </SUB> is actually the first value of a series {mu_0 (=mu_G), mu_1,ldots, mu_i,ldots} corresponding to successive period doublings of the orbits, which exhibit {1, 2, ldots, 2^i,ldots} cycles around L <SUB>4</SUB> or L <SUB>5</SUB>. Those orbits follow a Feigenbaum cascade leading to disappearance into chaos at a value {mu_infty = 0.0463004ldots} which generalizes Gascheau's work.

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