Regularization of the circular restricted three body problem on surfaces of constant curvature

DOI10.1007/s10884-017-9619-xzbMath1446.70021OpenAlexW2764037983MaRDI QIDQ1616366

Jaime Andrade, Ernesto Pérez-Chavela, Claudio Vidal

Publication date: 6 November 2018

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-017-9619-x

zbMATH Keywords

Hamiltonian formulationbinary collisionsurfaces of constant curvatureHill's regionlocal and global regularizationthe restricted three body problem

Mathematics Subject Classification ID

Three-body problems (70F07) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Dynamical systems methods for problems in mechanics (70G60)

Related Items (max. 100)

Equilibrium points in restricted problems on S2 and H2 ⋮ Local regularization of a restricted problem on \(H^2\) with primaries on hyperbolic motion ⋮ Hyperbolic regularization of the restricted three-body problem on curved spaces

Cites Work

• Relative equilibria of the curved \(N\)-body problem.
• The \(n\)-body problem in spaces of constant curvature. II: Singularities
• Kepler's problem in constant curvature spaces
• The restricted three body problem on surfaces of constant curvature
• Relative equilibria of the restricted three-body problem in curved spaces
• On the stability of tetrahedral relative equilibria in the positively curved 4-body problem
• On the singularities of the curved $n$-body problem
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature
• Libration points in spaces \(S^2\) and \(L^2\)
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