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The n-Body Problem in Spaces of Constant Curvature. Part II: Singularities

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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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Authors and Affiliations

  1. Pacific Institute for the Mathematical Sciences and Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, BC, Canada, V8W 3R4

    Florin Diacu

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Apdo. 55534, México, D.F., México

    Ernesto Pérez-Chavela

  3. Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, Canada, N2L 3C5

    Manuele Santoprete

Authors
  1. Florin Diacu
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  2. Ernesto Pérez-Chavela
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  3. Manuele Santoprete
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Correspondence to Florin Diacu.

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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

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