Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature

Abstract

AbstractWe classify and analyze the orbits of the Kepler problemon surfaces of constant curvature (both positive and negative, 𝕊2and ℍ2, respectively) as functions of the angular momentum and the energy. Hill's regions are characterized, and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum, and we describe the orbits of the regularized vector field. The phase portraits both for 𝕊2and ℍ2are pointed out.