Deprit's reduction of the nodes revisited

DOI10.1007/s10569-010-9329-8zbMath1270.70035OpenAlexW1971432484MaRDI QIDQ362636

Gabriella Pinzari, Luigi Chierchia

Publication date: 30 August 2013

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-010-9329-8

zbMATH Keywords

action-angle variables\(N\)-body problemdeprit reduction of the nodesplanetary systemsymplectic coordinates

Mathematics Subject Classification ID

Hamilton's equations (70H05) Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) (n)-body problems (70F10) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (11)

Regular and singular reductions in the spatial three-body problem ⋮ A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes ⋮ Euler integral and perihelion librations ⋮ The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori ⋮ Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem ⋮ Aspects of the planetary Birkhoff normal form ⋮ Flow reconstruction and invariant tori in the spatial three-body problem ⋮ Quasi-periodic solutions of the spatial lunar three-body problem ⋮ Partial reduction and Delaunay/Deprit variables ⋮ Canonical coordinates for the planetary problem ⋮ Global Kolmogorov tori in the planetary \(N\)-body problem. Announcement of result

Cites Work

• Planetary Birkhoff normal forms
• The planetary \(N\)-body problem: symplectic foliation, reductions and invariant tori
• Partial reduction in the \(N\)-body planetary problem using the angular momentum integral
• Elimination des noeuds dans le probleme newtonien des quatre corps
• Elimination of the nodes in problems ofn bodies

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