2018/06/27 by Pieter Tibboel, Tibboel, Pieter
Engineering · Physics and Astronomy · #Astro and Planetary Science #FOS: Physical sciences #Mathematical Physics (math-ph) #Space Satellite Systems and Control #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.1806.10379
openalex publication_date 2018/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove for a large class of n-body problems including a subclass of quasihomogeneous n-body problems, the classical n-body problem, the n-body problem in spaces of negative constant Gaussian curvature and a restricted case of the n-body problem in spaces of positive constant curvature for the case that all masses are equal and not necessarily constant that any solution for which the point masses move on a circle of not necessarily constant size has to be either a regular polygonal homographic orbit in flat space, or a regular polygonal rotopulsator in curved space, under the constraint that the minimal distance between point masses attains its minimum in finite time. Additionally, we prove that the same holds true if we add an extra mass at the center of that circle and find an explicit formula for the mass of each point particle in terms of the radius of the circle. Finally, we prove that for each order of the masses there is at most one polygonal homographic orbit for the case that the masses need not be constant.