CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

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

  Published:2016-06-17
 Printed: Oct 2017
  • Jaime Andrade,
    Departamento de Matemática, Facultad de Ciencias, Universidad de Bio-Bio, Casilla 5--C, Concepción, VIII--región, Chile
  • Nestor Dávila,
    Departamento de Matemática, Facultad de Ciencias, Universidad de Bio-Bio, Casilla 5--C, Concepción, VIII--región, Chile
  • Ernesto Pérez-Chavela,
    Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, (ITAM), Río Hondo 1, Col. Progreso Tizapán, Ciudad de México, 01080, México
  • Claudio Vidal,
    Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Departamento de Matemática, Facultad de Ciencias, Universidad de Bio-Bio, Casilla 5--C, Concepción, VIII--región, Chile
Format:   LaTeX   MathJax   PDF  

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 function of the angular momentum and the energy. Hill's region 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 portrait both for $\mathbb S^2$ and $\mathbb H^2$ are pointed out.
Keywords: Kepler problem on surfaces of constant curvature, Hill's region, singularities, regularization, qualitative analysis of ODE Kepler problem on surfaces of constant curvature, Hill's region, singularities, regularization, qualitative analysis of ODE
MSC Classifications: 70F16, 70G60 show english descriptions Collisions in celestial mechanics, regularization
Dynamical systems methods
70F16 - Collisions in celestial mechanics, regularization
70G60 - Dynamical systems methods
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/