The classical Kepler problem and geodesic motion on spaces of constant curvature

DOI10.1063/1.1324652zbMath0989.70005arXiv1411.5355OpenAlexW1978192911MaRDI QIDQ2731823

John F. L. Simmons, Aidan J. Keane, Richard Barrett

Publication date: 30 July 2001

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

Full work available at URL: https://arxiv.org/abs/1411.5355

zbMATH Keywords

energycanonical transformationHamiltonian vector fieldHamiltonian systemsphase flowgeodesic motionconstants of motionmass parameterRunge-Lenz vectorspaces of constant curvaturecurvature parameterclassical Kepler problemfamily of evolution spacesPoisson bracket Lie algebra

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Two-body problems (70F05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items

Conformal triality of the Kepler problem, Jacobi–Maupertuis metric and Kepler equation, Laplace–Runge–Lenz symmetry in general rotationally symmetric systems

Cites Work

• On the Geometry of the Kepler Problem
• On a ‘‘conformal’’ Kepler problem and its reduction
• Spectrum generating algebras and Lie groups in classical mechanics
• Two-body motion under the inverse square central force and equivalent geodesic flows
• The Kepler problem and geodesic flows in spaces of constant curvature
• Geodesic flow on an hyperboloid model and the two-body motion under repulsive Coulomb forces
• Regularization of kepler's problem and the averaging method on a manifold