The KS-transformation in hypercomplex form and the quantization of the negative-energy orbit manifold of the Kepler problem

DOI10.1007/BF01227489zbMath0586.70009OpenAlexW2061608468MaRDI QIDQ3711793

Maria Dina Vivarelli

Publication date: 1985

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01227489

zbMATH Keywords

quantizationquaternionsKepler problemsymplectic manifoldfull phase spaceHopf fibering of the spherehypercomplex KS-transformationKS- transformationmanifold of Kepler orbits of fixed negative energyquantum integrability condition

Mathematics Subject Classification ID

Celestial mechanics (70F15) Orbital mechanics (70M20)

Related Items (8)

Additive isometries on a quaternionic Hilbert space ⋮ Geometrical and physical outlook on the cross product of two quaternions ⋮ Iterative solution to perturbed Kepler problem via Kustaanheimo-Stiefel equation ⋮ Alternative angle-based approach to the \(\mathcal{KS}\)-map. An interpretation through symmetry and reduction ⋮ Additive functionals and operators on a quaternionic Hilbert space ⋮ On the connection among three classical mechanical problems via the hypercomplex KS-transformation ⋮ On a first integral of the Kepler problem ⋮ The Kepler problem: A unifying view

Cites Work

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• A new regularization of the restricted three-body problem and an application
• Miscellanea from the history of celestial mechanics
• The KS-transformation in hypercomplex form
• Regularization of kepler's problem and the averaging method on a manifold
• On nonclassical canonical systems
• On the regularization of the Kepler problem

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