Abstract
We analyze the singularities of the equations of motion and several types of singular solutions of the n-body problem in spaces of positive constant curvature. Apart from collisions, the equations encounter noncollision singularities, which occur when two or more bodies are antipodal. This conclusion leads, on the one hand, to hybrid solution singularities for as few as three bodies, whose orbits end up in a collision-antipodal configuration in finite time; on the other hand, it produces nonsingularity collisions, characterized by finite velocities and forces at the collision instant.
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Diacu, F., Pérez-Chavela, E. & Santoprete, M. The n-Body Problem in Spaces of Constant Curvature. Part II: Singularities. J Nonlinear Sci 22, 267–275 (2012). https://doi.org/10.1007/s00332-011-9117-y
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DOI: https://doi.org/10.1007/s00332-011-9117-y