Global phase portraits of the planar perpendicular problem of two fixed centers

DOI10.1063/1.3097195zbMath1214.37040OpenAlexW2054461800MaRDI QIDQ3650510

Jaume Llibre, Martín Vargas, Lidia Jiménez-Lara

Publication date: 14 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3097195

zbMATH Keywords

electric fieldsclassical mechanics

Mathematics Subject Classification ID

Three-body problems (70F07) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Cites Work

• Topology of the two-fixed-center problem
• The two fixed centers: an exceptional integrable system
• The problem of two fixed centers: bifurcations, actions, monodromy
• Phase portraits of the two-body problem with Manev potential
• Quantal two-center Coulomb problem treated by means of the phase-integral method. I. General theory
• Quantal two-center Coulomb problem treated by means of the phase-integral method. II. Quantization conditions in the symmetric case expressed in terms of complete elliptic integrals. Numerical illustration
• Quantal two-center Coulomb problem treated by means of the phase-integral method. III. Quantization conditions in the general case expressed in terms of complete elliptic integrals. Numerical illustration
• Differential Topology
• Topology of energy surfaces and existence of transversal Poincaré sections
• Topological analysis of the two-centre problem on the two-dimensional sphere

This page was built for publication: Global phase portraits of the planar perpendicular problem of two fixed centers