Regularization of the Circular Restricted Three Body Problem on Surfaces of Constant Curvature

  • Jaime Andrade
  • Ernesto Pérez-Chavela
  • Claudio Vidal


We consider a restricted three body problem on surfaces of constant curvature. As in the classical Newtonian case the collision singularities occur when the position particle with infinitesimal mass coincides with the position of one of the primaries. We prove that the singularities due to collision can be locally (each one separately) and globally (both as the same time) regularized through the construction of Levi-Civita and Birkhoff type transformations respectively. As an application we study some general properties of the Hill’s regions and we present some ejection–collision orbits for the symmetrical problem.


The restricted three body problem Surfaces of constant curvature Hamiltonian formulation Binary collision Local and global regularization Hill’s region 

Mathematics Subject Classification

Primary 70F07 Secondary 70G60 37D40 



Jaime Andrade was supported by a CONICYT fellowship (Chile). Ernesto Pérez-Chavela was partially supported by the Asociación Mexicana de Cultura A.C. This paper is part of Jaime Andrade Ph.D. thesis in the Program Doctorado en Matemática Aplicada, Universidad del Bío-Bío (Chile). The authors would like to thank the contributions of Martha Alvarez-Ramírez related to numerical simulations.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Jaime Andrade
    • 1
  • Ernesto Pérez-Chavela
    • 2
  • Claudio Vidal
    • 3
  1. 1.Departamento de Matemática, Facultad de CienciasUniversidad de Bío-BíoConcepción, VIII–regiónChile
  2. 2.Departamento de MatemáticasInstituto Tecnológico Autónomo de México, (ITAM)MexicoMexico
  3. 3.Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Departamento de Matemática, Facultad de CienciasUniversidad de Bío-BíoConcepción, VIII–regiónChile

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