Morse Index and Linear Stability of the Lagrangian Circular Orbit in a Three-Body-Type Problem Via Index Theory

@article{Barutello2014MorseIA,
  title={Morse Index and Linear Stability of the Lagrangian Circular Orbit in a Three-Body-Type Problem Via Index Theory},
  author={Vivina L. Barutello and Riccardo D. Jadanza and Alessandro Portaluri},
  journal={Archive for Rational Mechanics and Analysis},
  year={2014},
  volume={219},
  pages={387-444}
}
It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter β and on the eccentricity e of the orbit. We consider only the circular case (e = 0) but under the action of a broader family of singular potentials: α-homogeneous potentials, for $$\alpha \in (0, 2)$$α∈(0,2), and the logarithmic one. It turns out indeed that the Lagrangian circular orbit persists also in this more general setting. We discover a… 
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