Gravitational and harmonic oscillator potentials on surfaces of revolution

DOI10.1063/1.2912325zbMath1152.81602arXiv1305.3930OpenAlexW3100995975MaRDI QIDQ5504873

Manuele Santoprete

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/1305.3930

zbMATH Keywords

Kepler problemblock regularizationsurfaces of constant curvature 1

Mathematics Subject Classification ID

Kinematics of a particle (70B05)

Related Items (12)

The Bertrand's manifolds with equators ⋮ Darboux inversions of the Kepler problem ⋮ Keplerian Dynamics on the Heisenberg Group and Elsewhere ⋮ Algebra and Geometry Through Hamiltonian Systems ⋮ Superintegrable Bertrand natural mechanical systems ⋮ On the \(n\)-body problem on surfaces of revolution ⋮ Geometry, dynamics and different types of orbits ⋮ Bertrand surfaces with a pseudo-Riemannian metric of revolution ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ Block regularization of the Kepler problem on surfaces of revolution with positive constant curvature ⋮ The relations between the Bertrand, Bonnet, and Tannery classes ⋮ The explicit form of the Bertrand metric

Cites Work

• Kepler's problem in constant curvature spaces
• Superintegrable systems on a sphere
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
• 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)]
• Mixmaster Universe

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