On a ‘‘conformal’’ Kepler problem and its reduction

DOI10.1063/1.525105zbMath0467.70024OpenAlexW2049687575MaRDI QIDQ3920702

Toshihiro Iwai

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.525105

zbMATH Keywords

global aspectsconformal Kepler problemcommon energy surfacesreduction theorem for the symmetry groupsrelation of four-dimensional harmonic oscillator with three-dimensional Kepler problem

Mathematics Subject Classification ID

Hamilton's equations (70H05) Nonlinear dynamics in mechanics (70K99) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items

Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman-Deprit coordinates, The four-dimensional conformal Kepler problem reduces to the three-dimensional Kepler problem with a centrifugal potential and Dirac’s monopole field. Classical theory, On the trajectories of \(\mathrm{Sp}(1)\)-Kepler problems, The classical Kepler problem and geodesic motion on spaces of constant curvature, On the regularization of the Kepler problem, REDUCTION AND UNFOLDING: THE KEPLER PROBLEM, On the trajectories of O(1)-Kepler problems, Rydberg states of atoms and molecules. Basic group theoretical and topological analysis, On the three-dimensional lunar problem and other perturbation problems of the Kepler problem, The geometry of the SU(2) Kepler problem, The Kepler system as a reduced 4D harmonic oscillator, Quantization of the conformal Kepler problem and its application to the hydrogen atom

Cites Work

• Dynamical groups and spherical potentials in classical mechanics
• On the dynamical symmetries of the Kepler problem
• On reduction of the four-dimensional harmonic oscillator
• Regularization of kepler's problem and the averaging method on a manifold
• Symmetry transformations of the classical Kepler problem