On resonance

DOI10.1007/BF01234555zbMath0664.70034OpenAlexW4229676992MaRDI QIDQ3815602

No author found.

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1007/bf01234555

zbMATH Keywords

action-angle variablesformal solutionsresonant systemsHori's kernelKrylov-Bogolyubov first-order definition of averaging

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Celestial mechanics (70F15) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (1)

The implementation of Hori-Deprit method to the construction averaged planetary motion theory by means of computer algebra system Piranha

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Regular and stochastic motion
• On resonance in celestial mechanics
• Stability in the double resonance problem
• A second fundamental model for resonance
• The reduction to the rotation for planar perturbed Keplerian systems
• Motion of two planets with periods commensurable in the ratio 2?1 solutions of the hori auxiliary system
• A note on resonance in regular variables and averaging
• Resonance in regular variables I: Morphogenetic analysis of the orbits in the case of a first-order resonance
• The problem of small divisors in planetary motion
• Resonance in regular variables II: Formal solutions for central and non-central first-order resonance
• High-order resonances in the restricted three-body problem
• A problem of libration with two degrees of freedom
• The reducing transformation and Apocentric Librators
• Canonical solution of the two critical argument problem
• The critical inclination in artificial satellite theory
• A comparison of the Bohlin-von Zeipel and Bohlin-Lie series methods in resonant systems
• A theory of libration
• Matched Asymptotic Expansions in the Two-body Problem with Quick Loss of Mass
• Formal integrals for an autonomous Hamiltonian system near an equilibrium point
• A theory of integration for the extended Delaunay method
• A perturbation method for problems with two critical arguments
• Canonical transformations depending on a small parameter
• A new algorithm for the Lie transformation
• A second-order solution of the Ideal Resonance Problem by Lie series
• Ignorable coordinates in the ideal resonance problem
• Averaging methods in nonlinear dynamical systems

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