On the three-dimensional lunar problem and other perturbation problems of the Kepler problem

DOI10.1016/0022-247X(83)90224-XzbMath0569.70013OpenAlexW1967151874MaRDI QIDQ1060876

B. George

Publication date: 1983

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(83)90224-x

zbMATH Keywords

regularizationKepler problemKAM-theoryJacobian constantaction-angle-variablesexistence of quasiperiodic solutionsspinor regularizationthree-dimensional restricted problem of three bodiestwo and three basic frequencies

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Celestial mechanics (70F15)

Related Items

A group theoretical approach to a certain class of perturbations of the Kepler problem, Constrained normalization of Hamiltonian systems and perturbed Keplerian motion, Reduction of degenerate Lagrangian systems, Generalized Hopf fibration and geometric \(\mathrm{SO}(3)\) reduction of the \(4\mathrm{DOF}\) harmonic oscillator, Closed-form normalizations of perturbed two-body problems., On resonant classical Hamiltonians with n frequencies, Dynamical and symmetry groups of the \(SU (2)\) Kepler problem, On the regularization of the Kepler problem, A family of periodic orbits in the three-dimensional lunar problem, Normal forms for perturbed Keplerian systems., The geometry of the SU(2) Kepler problem, The Kepler system as a reduced 4D harmonic oscillator

Cites Work

• Recollections of Jürgen Moser
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• On a ‘‘conformal’’ Kepler problem and its reduction
• Das Oszillator-Kepler Problem und die Lie-Algebra.
• On some new long periodic solutions of the plane restricted three body problem
• Perturbation theory of Kepler motion based on spinor regularization.
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• On the Theory of Quasiperiodic Motions
• On the regularization of the Kepler problem
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