On the stability of periodic N-body motions with the symmetry of Platonic polyhedra
arXiv:1801.06429 · doi:10.1088/1361-6544/aad644
Abstract
In (Fusco et. al., 2011) several periodic orbits of the Newtonian N-body problem have been found as minimizers of the Lagrangian action in suitable sets of T-periodic loops, for a given T>0. Each of them share the symmetry of one Platonic polyhedron. In this paper we first present an algorithm to enumerate all the orbits that can be found following the proof in (Fusco et. al., 2011). Then we describe a procedure aimed to compute them and study their stability. Our computations suggest that all these periodic orbits are unstable. For some cases we produce a computer-assisted proof of their instability using multiple precision interval arithmetic.
References in corpus (5)
- On the Existence of Collisionless Equivariant Minimizers for the Classical n-body Problem
- Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry
- An existence of simple choreographies for N-body problem - a computer assisted proof
- Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory
- A dihedral Bott-type iteration formula and stability of symmetric periodic orbits