Spacecraft Dynamics and Control
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Abstract
Abstract
Abstract We show the existence of a new symmetric spatial central configuration for the 8-body problem: two rhombi rotated by $$\pi /2$$ π / 2 relative to each other around a diagonal of one of the rhombi. More specifically: (i) six bodies are in a plane, four of which are collinear and symmetrically positioned with respect to the midpoint of the segment containing them, and two bodies are symmetrically positioned on a segment orthogonal to the previous one; (ii) the other two bodies are symmetrically positioned on a segment orthogonal to the plane containing the six previous bodies. The obtained results have simple and analytic proofs. Some numerical simulations are also presented.
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@article{Fernandes2026Rhomboidal,
title = {Bi-Rhomboidal Spatial Central Configuration for the Eight-Body Problem},
author = {Antônio Carlos Fernandes and Luis Fernando Mello},
journal = {Journal of Nonlinear Science},
year = {2026},
doi = {10.1007/s00332-026-10303-6},
url = {https://doi.org/10.1007/s00332-026-10303-6}
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