Local minimality properties of circular motions in $$1/r^\alpha $$ potentials and of the figure-eight solution of the 3-body problem

@article{Fenucci2022LocalMP,
  title={Local minimality properties of circular motions in \$\$1/r^\alpha \$\$ potentials and of the figure-eight solution of the 3-body problem},
  author={Marco Fenucci},
  journal={Partial Differential Equations and Applications},
  year={2022}
}
  • M. Fenucci
  • Published 4 January 2022
  • Mathematics
  • Partial Differential Equations and Applications
We first take into account variational problems with periodic boundary conditions, and briefly recall some sufficient conditions for a periodic solution of the Euler-Lagrange equation to be either a directional, a weak, or a strong local minimizer. We then apply the theory to circular orbits of the Kepler problem with potentials of type 1/r, α > 0. By using numerical computations, we show that circular solutions are strong local minimizers for α > 1, while they are saddle points for α ∈ (0, 1… 
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