Laplace-Runge-Lenz symmetry in general rotationally symmetric systems

Abstract

The universality of the Laplace-Runge-Lenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets. Generalized Laplace-Runge-Lenz vectors are definable to be constant (not only piece-wise conserved) for all cases, including systems with open orbits. Applications are included for relativistic Coulomb systems and electromagnetic/gravitational systems in the post-Newtonian approximation. The evidence for the relativistic origin of the symmetry are extended to all centrally symmetric systems.

References in corpus (3)

• The MICZ-Kepler Problems in All Dimensions
• Unfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential
• The classical Kepler problem and geodesic motion on spaces of constant curvature

Cited by in corpus (8)

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• Centre-of-mass and internal symmetries in classical relativistic systems
• Back to epicycles - relativistic Coulomb systems in velocity space
• Hamilton symmetry in relativistic Coulomb systems
• Complex functions and geometric structures associated to the superintegrable Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion