arXiv subjects

Allyson Oliveira

Publications and source records attributed to Allyson Oliveira.

3 recordsLinked to original sources

arXiv2015

Central configurations of the spatial seven-body problem: two twisted triangles plus one

In this work we are interested in the central configurations of the spatial seven-body problem where six of them are at vertices of two congruents equilateral triangles belong to parallel planes and one triangle is a rotation by the angle $π/3$ from the other one. We show a existence and uniqueness of a class of central configuration with this shape, namely six bodies with equal masses at the vertice of a regular octahedron with the seventh body in its center. There is not restriction to the mass of the seventh body.

math.MG↗

arXiv2012

Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a stacked central configuration too. We show that the configuration are necessarily symmetric and the other sattelites has the same mass. Moreover we proved that the number of central configuration in this case is in general one, two or three and in the special case where the satellites diametrically opposite have the same mass we proved that the number of central configuration is one or two saying the exact value of the ratio of the masses that provides this bifurcation.

math.DS↗

arXiv2011

On stacked central configuration of the planar coorbital satellites problem

In this work we look for central configurations of the planar 1 + n body problem such that, after the addition of one or two satellites, we have a new planar central configuration. We determine all such configurations in two cases: the first, the addition of two satellites considering that all satellites have equal infinitesimal masses and the second case where one satellite is added but the infinitesimal masses are not necessarily equal.

math.DS↗