The central configurations of four masses x, -x, y, -y
| dc.creator | Celli, Martin | |
| dc.date | 2006-09-20 | |
| dc.date.accessioned | 2026-07-07T07:25:02Z | |
| dc.date.available | 2026-07-07T07:25:02Z | |
| dc.description | The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, -x, y, -y with x different from y (a parallelogram and two trapezoids) and two planar non-collinear central configurations for masses x, -x, x, -x (two diamonds). Except the case studied here, the only known case where the four-body central configurations with non-vanishing masses can be listed is the case with equal masses (Albouy, 1996), which requires the use of a symbolic computation program. Thanks to a lemma used in the proof of our result, we also show that a co-circular four-body central configuration has non-vanishing total mass or vanishing multiplier. | |
| dc.identifier | https://arxiv.org/abs/math/0609578 | |
| dc.identifier | http://arxiv.org/abs/math/0609578 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116592 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 34C05 | |
| dc.title | The central configurations of four masses x, -x, y, -y | |
| dc.type | text |