# Attracting and Repelling 2-Body Problems on a Family of Surfaces of Constant Curvature

@article{GarciaNaranjo2020AttractingAR, title={Attracting and Repelling 2-Body Problems on a Family of Surfaces of Constant Curvature}, author={Luis C. Garc'ia-Naranjo and James Montaldi}, journal={Journal of Dynamics and Differential Equations}, year={2020}, pages={1-25} }

We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric equivalence between repelling particles and attracting particles, and relying on previous work on the similar classification for attracting particles. The second theme of the paper is to study the 2-body problem on a surface of constant curvature treating the curvature as a parameter, and with particular interest in…

## 2 Citations

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The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galperin [Comm. Math.…

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