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

Pedro Pablo Ortega Palencia, Ruben Dario Ortiz Ortiz and Ana Magnolia Marin Ramirez
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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

Mathematics, 2021, vol. 9, issue 5, 1-8

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 .

Keywords: center of mass; conformal metric; geodesic; hyperbolic lever law (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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