Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature. (1st October 2017)

• Record Type: Journal Article
• Authors: Andrade, Jaime; Dàvila, Nestor; Pérez-Chavela, Ernesto; Vidal, Claudio
• Is Part Of: Canadian journal of mathematics. Volume 69:Number 5(2017)
• Page Start: 961
• Page End: 991
• Publication Date: 2017-10-01
• Subjects: 70F16 -- 70G60; Kepler problem on surfaces of constant curvature -- Hill's region -- singularities -- regularization -- qualitative analysis of ODE; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2016-014-5
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: We classify and analyze the orbits of the Kepler problem on surfaces of constant curvature (both positive and negative, ${{\mathbb{S}}^{2}}$ and ${{\mathbb{H}}^{2}}$, 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 ${{\mathbb{S}}^{2}}$ and ${{\mathbb{H}}^{2}}$ are pointed out.