Abstract
We review some recently discovered periodic orbits of the N-body problem [8], whose existence is proved bymeans of variational methods. These orbits are minimizers of the Lagrangian action functional in a set of T-periodic loops, equivariant for the action of a group G and satisfying some topological constraints. Both the group action and the topological constraints are defined using the symmetry of Platonic polyhedra.
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Notes
- 1.
1 Indeed for ℛ = ℐ all sides are of the same kind.
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Gronchi, G.F. (2014). Periodic Orbits of the N-body Problem with the Symmetry of Platonic Polyhedra. In: Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds) Mathematical Models and Methods for Planet Earth. Springer INdAM Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-02657-2_12
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