Equivariant optimisation for the gravitational $n$-body problem: a computational factory of symmetric orbits
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912083961970688 |
|---|---|
| author | Barutello, Vivina Bergomi, Mattia G. Canneori, Gian Marco Ciccarelli, Roberto Ferrario, Davide L. Terracini, Susanna Vertechi, Pietro |
| author_facet | Barutello, Vivina Bergomi, Mattia G. Canneori, Gian Marco Ciccarelli, Roberto Ferrario, Davide L. Terracini, Susanna Vertechi, Pietro |
| contents | In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other interacting particles models. Among all, it prepares for large-scale search of symmetric periodic orbits for the classical $n$-body problem and their classification, paving the way towards a computational validation of Poincaré conjecture about the density of periodic orbits. Through the accessible language of Julia, \texttt{SymOrb.jl} offers a unified implementation of an earlier version. This paper provides theoretical and practical guidelines for the specific approach we adopt, complemented with examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant optimisation for the gravitational $n$-body problem: a computational factory of symmetric orbits Barutello, Vivina Bergomi, Mattia G. Canneori, Gian Marco Ciccarelli, Roberto Ferrario, Davide L. Terracini, Susanna Vertechi, Pietro Dynamical Systems 70F10, 70-08, 37C81, 65K10, 65L10 In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other interacting particles models. Among all, it prepares for large-scale search of symmetric periodic orbits for the classical $n$-body problem and their classification, paving the way towards a computational validation of Poincaré conjecture about the density of periodic orbits. Through the accessible language of Julia, \texttt{SymOrb.jl} offers a unified implementation of an earlier version. This paper provides theoretical and practical guidelines for the specific approach we adopt, complemented with examples. |
| title | Equivariant optimisation for the gravitational $n$-body problem: a computational factory of symmetric orbits |
| topic | Dynamical Systems 70F10, 70-08, 37C81, 65K10, 65L10 |
| url | https://arxiv.org/abs/2410.17861 |