Response to “Comment on ‘Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2’ ” [J. Math. Phys. 46, 052702 (2005)]

DOI10.1063/1.2107287zbMath1111.70006OpenAlexW2051717161MaRDI QIDQ3438696

Mariano Santander, José F. Cariñena, Manuel F. Rañada

Publication date: 16 May 2007

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

Full work available at URL: https://doi.org/10.1063/1.2107287

Mathematics Subject Classification ID

Two-body problems (70F05) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items

Finiteness of polygonal relative equilibria for generalised quasi-homogeneous \(n\)-body problems and \(n\)-body problems in spaces of constant curvature ⋮ Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 ⋮ The restricted three body problem on surfaces of constant curvature ⋮ The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories ⋮ Projective dynamics and classical gravitation ⋮ Some remarks about the centre of mass of two particles in spaces of constant curvature ⋮ Some results on the existence and multiplicity of Dirichlet type solutions for a singular equation coming from a Kepler problem on the sphere ⋮ A maximally superintegrable system on an \(n\)-dimensional space of nonconstant curvature ⋮ Study of the ``non-abelian current algebra of a non-linear \(\sigma \)-model ⋮ Variational property of periodic Kepler orbits in constant curvature spaces ⋮ Stability of the polar equilibria in a restricted three-body problem on the sphere ⋮ Global symplectic regularization for some restricted 3-body problems on \(S^1\) ⋮ An intrinsic approach in the curved $n$-body problem. The positive curvature case

Cites Work

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• Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
• On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2
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• Separable Potentials and a Triality in Two-Dimensional Spaces of Constant Curvature