https://doi.org/10.1140/epjp/s13360-024-04855-3
Regular Article
Analysis of the geometry of the zero-velocity curves in the N-body ring problem depending on the mass ratio parameter
Department of Applied Mathematics, University of Alicante, Alicante, Spain
Received:
4
October
2023
Accepted:
1
January
2024
Published online:
20
January
2024
The purpose of the present study is the investigation of the effect of the mass ratio parameter, 
, on the geometry of the zero-velocity curves, when there are 
peripheral bodies. It is well known that there is a bifurcation value of the parameter in the N-body ring problem that produces a change in the number of stationary solutions in the system from 5N to 3N. By examining the behavior of the critical values of the Jacobi constant that define each of the zones of stationary solutions, we have unveiled the existence of other bifurcations or critical values of in the scenario with 5N stationary solutions, which cause different changes in the geometry of the zero-velocity curves, which in turn affect the threshold for the total opening of the curves of zero velocity.
© The Author(s) 2024
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