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- Title
Asymptotic relative equilibrium in the n-body problem: Relativistic application in the Poincaré upper half-plane.
- Authors
Ortiz, Ruben Dario Ortiz; Caro, Mario Enrique Almanza; Perez, Alejandra Patricia Guzman; Ramirez, Ana Magnolia Marin
- Abstract
In this paper, we study the n -body problem in the Poincaré upper half-plane ℍ R 2 , where the radius R of the Poincaré disk is fixed. We introduce a new potential to derive the condition for hyperbolic relative equilibria on ℍ R 2 . We analyze the relative equilibrium of positive masses moving along geodesics under the SL (2 , ℝ) group. This result is utilized to establish the existence of relative equilibria for the n -body problem on ℍ R 2 for n = 2 and n = 3. We revisit previously known results and uncover new qualitative findings on relative equilibria that are not evident in an extrinsic context. Additionally, we provide a simple expression for the center of mass of a system of point particles on a two-dimensional surface with negative constant Gaussian curvature.
- Subjects
MANY-body problem; GAUSSIAN curvature; CENTER of mass; EQUILIBRIUM; GEODESICS; SPHERICAL projection
- Publication
International Journal of Geometric Methods in Modern Physics, 2024, Vol 21, Issue 1, p1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887824500531