# 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 $$n=4,5,6$$
.

## 5 Citations

Filaments and voids in planar central configurations

- Mathematics
- 2021

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

- PhysicsCelestial Mechanics and Dynamical Astronomy
- 2022

<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

- Mathematics, PhysicsArXiv
- 2022

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…

Central configurations on the plane with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e485" altimg="si6.svg"><mml:mi>N</mml:mi></mml:math> heavy and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e490" altimg="si7.svg"><mml:mi>k</mm

- ArtCommunications in Nonlinear Science and Numerical Simulation
- 2022

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<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…