Runge–Lenz vector as a 3d projection of SO(4) moment map in R4×R4 phase space

DOI10.1088/1751-8121/ACCEE7zbMath1530.37081arXiv2212.04931OpenAlexW4366495709MaRDI QIDQ6041778

Unnamed Author, Toshiro Sato, Hitoshi Ikemori, Shinsaku Kitakado

Publication date: 15 May 2023

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

Full work available at URL: https://arxiv.org/abs/2212.04931

zbMATH Keywords

moment mapRunge-Lenz vectorKepler systemKustaanheimo-Stiefel transformation

Mathematics Subject Classification ID

Two-body problems (70F05) Momentum maps; symplectic reduction (53D20) Orbital mechanics (70M20) Dynamical systems in classical and celestial mechanics (37N05) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (1)

Milankovitch equations with spinors

Cites Work

• Reduction of symplectic manifolds with symmetry
• The four-dimensional conformal Kepler problem reduces to the three-dimensional Kepler problem with a centrifugal potential and Dirac’s monopole field. Classical theory
• Stäckel-Equivalent Integrable Hamiltonian Systems
• Integrals, invariant manifolds, and degeneracy for central force problems in R n
• The Kustaanheimo–Stiefel transformation in geometric algebra
• Quantum Theory, Groups and Representations
• Superintegrable systems with spin induced by co-algebra symmetry
• Perturbation theory of Kepler motion based on spinor regularization.

This page was built for publication: Runge–Lenz vector as a 3d projection of SO(4) moment map in R4×R4 phase space