Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses

@article{Moczurad2020CentralCI,
  title={Central configurations in the spatial n-body problem for \$\$n=5,6\$\$ with equal masses},
  author={Małgorzata Moczurad and Piotr Zgliczyński},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={2020},
  volume={132},
  pages={1-27}
}
We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for $$n=5$$ and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for $$n=4,5,6,7$$ and in the spatial case for $$n=4,5,6$$ . 
Filaments and voids in planar central configurations
We have numerically computed planar central configurations of n = 1000 bodies of equal masses. A classification of central configurations is proposed based on the numerical value of the complexity,
A stochastic optimization algorithm for analyzing planar central and balanced configurations in the n-body problem
<jats:p>A stochastic optimization algorithm for analyzing planar central and balanced configurations in the <jats:italic>n</jats:italic>-body problem is presented. We find a comprehensive list of
A numerical analysis of planar central and balanced configurations in the (n+1)-body problem with a small mass
Two numerical algorithms for analyzing planar central and balanced configurations in the ( n + 1) -body problem with a small mass are pre-sented. The first one relies on a direct solution method of the

References

SHOWING 1-10 OF 24 REFERENCES
Central configurations in planar $N$-body problem for $N=5,6,7$ with equal masses
We give a computer assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for n = 5, 6, 7 with equal masses. We show all these central
On the spatial central configurations of the 5--body problem andtheir bifurcations
Central configurations provide special solutions of the general $n$--body problem. Using the mutual distances between the $n$ bodies as coordinates we study the bifurcations of the spatial central
Central configurations of the 5-body problem with equal masses in three-dimensional space
We enumerate central configurations with axial symmetry in the 5-body problem with equal masses in three-dimensional space. It is thus shown, that only two of these configurations, have a unique
Central configurations of the five-body problem with equal masses
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to
Central Configurations of the 5-Body Problem with Equal Masses in Three-Space
Central configurations with axial symmetry in the 5-body problem with equal masses in three-space are enumerated. It is shown that only two of the configurations have a unique symmetry axis. Symbolic
Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses
TLDR
A more general statement of the algebraic part of a symmetry theorem for the central configurations of the newtonian spatial 5-body problem with equal masses is proved, valid for a class of potentials defined by functions with increasing and concave derivatives.
Relative equilibrium solutions in the four body problem
Beyond the casen=3 little was known about relative equilibrium solutions of then-body problem up to recent years. Palmore's work provides in the general case much useful information. In the casen=4
Finiteness of spatial central configurations in the five-body problem
We strengthen a generic finiteness result due to Moeckel by showing that the number of spatial central configurations of the Newtonian five-body problem with positive masses is finite, apart from
Generic Finiteness for Dziobek Configurations
The goal of this paper is to show that for almost all choices of n masses, mi, there are only finitely many central configurations of the Newtonian n-body problem for which the bodies span a space of
Central configurations in planar n-body problem with equal masses for $$n=5,6,7$$
<jats:p>We give a computer-assisted proof of the full listing of central configuration for <jats:italic>n</jats:italic>-body problem for Newtonian potential on the plane for
...
...