Symmetry of the restricted 4 + 1 body problem with equal masses |
| |
Authors: | A A Santos C Vidal |
| |
Institution: | (1) Departamento de Matemática, Universidade Federal de Sergipe, Av. Marechal Rondon, s/n, Jardim Rosa Elze, Sāo Cristóvāo-SE, CEP, 49100-000, Brazil;(2) Departamento de Maternática, Facultad de Ciencias, Universidad del Bío Bío, Casilla 5-C, Concepción, VIII-Región, Chile |
| |
Abstract: | We consider the problem of symmetry of the central configurations in the restricted 4 + 1 body problem when the four positive
masses are equal and disposed in symmetric configurations, namely, on a line, at the vertices of a square, at the vertices
of a equilateral triangle with a mass at the barycenter, and finally, at the vertices of a regular tetrahedron 1–3]. In these
situations, we show that in order to form a non collinear central configuration of the restricted 4 + 1 body problem, the
null mass must be on an axis of symmetry. In our approach, we will use as the main tool the quadratic forms introduced by
A. Albouy and A. Chenciner 4]. Our arguments are general enough, so that we can consider the generalized Newtonian potential
and even the logarithmic case. To get our results, we identify some properties of the Newtonian potential (in fact, of the
function ϕ(s) = −s
k, with k < 0) which are crucial in the proof of the symmetry. |
| |
Keywords: | 37C75 34D20 34A25 |
本文献已被 SpringerLink 等数据库收录! |
|