The ideal resonance problem a comparison of two formal solutions I

DOI10.1007/BF01235818zbMath0596.70025OpenAlexW4240478758MaRDI QIDQ3730057

Ali Y. Abdulla, A. H. Jupp

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1007/bf01235818

zbMATH Keywords

variablesformal solutiondirect numerical integrationPoincareideal resonance problemLie series expansionperturbed simple pendulum

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Hamilton's equations (70H05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (6)

Application of the extended Delaunay method to the ideal resonance problem ⋮ The ideal resonance problem a comparison of two formal solutions III ⋮ Relativistic effects in the critical inclination problem in artificial satellite theory ⋮ A new approach to the librational solution in the Ideal Resonance Problem ⋮ A fourth-order solution of the ideal resonance ⋮ A geometric approach to the Ideal Resonance Problem

Cites Work

• Numerical calculation of elliptic integrals and elliptic functions
• On resonance in celestial mechanics
• A resonance problem of two degrees of freedom
• Theory of the Trojan asteroids, IV
• A second-order global solution of the ideal resonance problem
• The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions
• A second-order solution of the Ideal Resonance Problem by Lie series

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