A new class of pyramidal central configurations for spatial Newtonian 6-body problems

@misc{ding2026class,
  title = {{A new class of pyramidal central configurations for spatial Newtonian 6-body problems}},
  author = {Liang Ding and Jin Wang and Jinrong Wang and Zhifu Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24445},
  eprint = {2610.24445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24445},
}

TY  - UNPB
TI  - A new class of pyramidal central configurations for spatial Newtonian 6-body problems
AU  - Liang Ding
AU  - Jin Wang
AU  - Jinrong Wang
AU  - Zhifu Xie
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24445
UR  - https://arxiv.org/abs/2610.24445
AB  - While a non-concyclic rhombus can support a central configuration in the planar Newtonian four-body problem, such a configuration cannot serve as the base of a pyramidal central configuration in the spatial five-body problem. In this paper, we establish the existence of a new class of pyramidal central configurations in the spatial Newtonian six-body problem, characterized by a non-concyclic quadrilateral base. This geometric structure distinguishes the new configurations from the known pyramidal central configurations of the spatial five-body problem. We investigate several fundamental properties of these configurations and provide numerical examples illustrating the theoretical results in each case. Furthermore, we demonstrate that this new class of central configurations can be used to construct perverse solutions in three-dimensional space, revealing an additional connection between the geometry of central configurations and the dynamics of the Newtonian N-body problem.
ER  -