Families of periodic solutions of the 4- and 6-body problem using a gradient-free continuation method
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915920382787584 |
|---|---|
| author | Perdomo, Oscar |
| author_facet | Perdomo, Oscar |
| contents | In this paper, we describe a gradient-free method to solve a system of equations, and we use it to construct two families of pseudo-periodic planar solutions of the 4- and 6-body problem. The method is a stochastic black-box procedure that uses only function evaluations. For the 4-body problem, bodies 1 and 2 have mass 1 and move opposite to each other, and bodies 3 and 4 have mass $m_2$ and also move opposite to each other. For the 6-body problem, bodies 1, 2, and 3 have mass 1 and move on the vertices of an equilateral triangle centered at the origin, and bodies 4, 5, and 6 have mass $m_2$ and also move on the vertices of an equilateral triangle. In both cases, we compute families of periodic solutions by imposing return conditions up to rotation and relabeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Families of periodic solutions of the 4- and 6-body problem using a gradient-free continuation method Perdomo, Oscar Dynamical Systems Mathematical Physics 70F10 (Primary), 70F15, 37N05 (Secondary) In this paper, we describe a gradient-free method to solve a system of equations, and we use it to construct two families of pseudo-periodic planar solutions of the 4- and 6-body problem. The method is a stochastic black-box procedure that uses only function evaluations. For the 4-body problem, bodies 1 and 2 have mass 1 and move opposite to each other, and bodies 3 and 4 have mass $m_2$ and also move opposite to each other. For the 6-body problem, bodies 1, 2, and 3 have mass 1 and move on the vertices of an equilateral triangle centered at the origin, and bodies 4, 5, and 6 have mass $m_2$ and also move on the vertices of an equilateral triangle. In both cases, we compute families of periodic solutions by imposing return conditions up to rotation and relabeling. |
| title | Families of periodic solutions of the 4- and 6-body problem using a gradient-free continuation method |
| topic | Dynamical Systems Mathematical Physics 70F10 (Primary), 70F15, 37N05 (Secondary) |
| url | https://arxiv.org/abs/2604.05653 |