Regular and singular reductions in the spatial three-body problem

DOI10.1007/s12346-012-0083-zzbMath1282.70016OpenAlexW2047801108MaRDI QIDQ2393365

Flora Sayas, Patricia Yanguas, Jesús F. Palacián

Publication date: 7 August 2013

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-012-0083-z

zbMATH Keywords

relative equilibriastability and bifurcationscontinuous symmetriesregular and singular reductionsspatial three-body problemDelaunay and deprit's coordinatesinvariants and Gröbner basesJacobi elimination of the nodesnormalising over the Mean anomaliesreduced phase spaces and reduced Hamiltonians

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Three-body problems (70F07) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (15)

Reduced 4D oscillators and orbital elements in Keplerian systems: Cushman-Deprit coordinates ⋮ On the co-existence of maximal and whiskered tori in the planetary three-body problem ⋮ Integrability of close encounters in the spatial restricted three-body problem ⋮ KAM in generalized Hamiltonian systems with multi-scales ⋮ Quasiperiodic Poincaré persistence at high degeneracy ⋮ Poincaré-Treshchev mechanism in multi-scale, nearly integrable Hamiltonian systems ⋮ Aspects of the planetary Birkhoff normal form ⋮ Normalization through invariants in \(n\)-dimensional Kepler problems ⋮ Lower-dimensional tori in multi-scale, nearly integrable Hamiltonian systems ⋮ Multiscale KAM theorem for Hamiltonian systems ⋮ Flow reconstruction and invariant tori in the spatial three-body problem ⋮ A first integral to the partially averaged Newtonian potential of the three-body problem ⋮ Lower dimension tori of general types in multi-scale Hamiltonian systems ⋮ Kustaanheimo-Stiefel regularization and the quadrupolar conjugacy ⋮ Quasi-periodic solutions of the spatial lunar three-body problem

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