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Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Author

Listed:
  • Pedro Pablo Ortega Palencia

    (Grupo Ecuaciones Diferenciales, Universidad de Cartagena, Cartagena de Indias 130014, Colombia)

  • Ruben Dario Ortiz Ortiz

    (Grupo Ondas, Universidad de Cartagena, Cartagena de Indias 130014, Colombia)

  • Ana Magnolia Marin Ramirez

    (Grupo Ondas, Universidad de Cartagena, Cartagena de Indias 130014, Colombia)

Abstract

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere L R 1 .

Suggested Citation

  • Pedro Pablo Ortega Palencia & Ruben Dario Ortiz Ortiz & Ana Magnolia Marin Ramirez, 2021. "Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem," Mathematics, MDPI, vol. 9(5), pages 1-8, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:531-:d:509906
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    Cited by:

    1. Rubén Darío Ortiz Ortiz & Ana Magnolia Marín Ramírez & Ismael Oviedo de Julián, 2024. "Asymptotic Antipodal Solutions as the Limit of Elliptic Relative Equilibria for the Two- and n-Body Problems in the Two-Dimensional Conformal Sphere," Mathematics, MDPI, vol. 12(7), pages 1-17, March.

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