A geometric approach to the Ideal Resonance Problem

DOI10.1007/BF01235537zbMath0688.70021OpenAlexW2060104962MaRDI QIDQ4207630

Jacques Henrard, Pascal Wauthier

Publication date: 1988

Published in: Celestial Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01235537

zbMATH Keywords

action-angle variablescoordinate transformationpseudo-timeimplicit `Kepler equationpendulum perturbations

Mathematics Subject Classification ID

Hamilton's equations (70H05) Two-body problems (70F05) Free motions in linear vibration theory (70J30)

Related Items (4)

Exact solution of a triaxial gyrostat with one rotor ⋮ Slow crossing of a stochastic layer ⋮ A fourth-order solution of the ideal resonance ⋮ Synchronization of perturbed non-linear Hamiltonians

Cites Work

• Unnamed Item
• On resonance in celestial mechanics
• A second fundamental model for resonance
• Resonance in regular variables I: Morphogenetic analysis of the orbits in the case of a first-order resonance
• Resonance in regular variables II: Formal solutions for central and non-central first-order resonance
• The ideal resonance problem a comparison of two formal solutions I
• A new approach to the librational solution in the Ideal Resonance Problem
• A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems
• The elimination of the parallax in satellite theory
• A second-order global solution of the ideal resonance problem
• A theory of libration
• Hopf-Friedrichs bifurcation and the hunting of a railway axle
• A perturbation method for problems with two critical arguments
• The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions
• Canonical transformations depending on a small parameter
• On a perturbation theory using Lie transforms
• A second-order solution of the Ideal Resonance Problem by Lie series
• Regularization in the Ideal Resonance Problem
• Normality condition in the ideal resonance problem
• Perturbation method in the theory of nonlinear oscillations
• The perturbed ideal resonance problem

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