Reduction of the classical MICZ-Kepler problem to a two-dimensional linear isotropic harmonic oscillator

DOI10.1063/1.1781748zbMath1071.70006OpenAlexW1990047012MaRDI QIDQ4833502

Maria Clara Nucci, Peter G. L. Leach

Publication date: 15 December 2004

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

Full work available at URL: https://doi.org/10.1063/1.1781748

Mathematics Subject Classification ID

Two-body problems (70F05) Motion of charged particles (78A35) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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Uses Software

• REDUCE

Cites Work

• Integrals of motion for the classical two-body problem with drag
• Linearization criteria for a system of second-order ordinary differential equations
• Hurwitz transformation and oscillator representation of a 5D ``isospin particle
• The determination of nonlocal symmetries by the technique of reduction of order
• The quantized \(\text{SU}(2)\) Kepler problem and its symmetry group for negative energies
• Integration of second order ordinary differential equations not possessing Lie point symmetries
• Canonical forms for systems of two second-order ordinary differential equations
• The harmony in the Kepler and related problems
• The first integrals and orbit equation for the Kepler problem with drag
• New Integrable Family inn-Dimensional Homogeneous Lotka–Volterra Systems with Abelian Lie Algebra
• Kepler-type dynamical symmetries of long-range monopole interactions
• Symmetries of differential equations. IV
• Lie point symmetries for systems of second order linear ordinary differential equations
• Geometric quantisation of the MIC-Kepler problem
• An algebraic and geometric approach to non-bijective quadratic transformations
• Lie algebras under constraints and non-bijective canonical transformations
• The algebraic structure of generalized Ermakov systems in three dimensions
• On the complete symmetry group of the classical Kepler system
• Coherent states map for MIC–Kepler system
• 8D oscillator and 5D Kepler problem: The case of nontrivial constraints
• An analytic solution to the classical two-body problem with drag
• A Necessary Condition for Existence of Lie Symmetries in General Systems of Ordinary Differential Equations
• Lie point symmetries and first integrals: The Kowalevski top
• The Ermanno–Bernoulli constants and representations of the complete symmetry group of the Kepler problem
• Quantization of the multifold Kepler system
• The complete Kepler group can be derived by Lie group analysis
• The Economy of Complete Symmetry Groups for Linear Higher Dimensional Systems

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