A Canonical Transformation to Eliminate Resonant Perturbations. I

• Published in: The Astronomical journal Vol. 162; no. 1; pp. 22 - 32
• Main Authors: Deme, Barnabás, Kocsis, Bence
• Format: Journal Article
• Language: English
• Published: Madison The American Astronomical Society 01.07.2021; IOP Publishing
• Subjects: ALGORITHMS; Astronomy; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CANONICAL TRANSFORMATIONS; Celestial mechanics; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DYNAMICAL SYSTEMS; HAMILTONIANS; HARMONIC OSCILLATORS; HARMONICS; Integrators; MECHANICS; Orbital mechanics; Orbital resonances (celestial mechanics); ORBITS; OSCILLATORS; Perturbation; Resonance; THREE-BODY PROBLEM; Transformations (mathematics)

We study dynamical systems that admit action-angle variables at leading order, which are subject to nearly resonant perturbations. If the frequencies characterizing the unperturbed system are not in resonance, the long-term dynamical evolution may be integrated by orbit-averaging over the high-frequ...