Wisdom system: dynamics in the adiabatic approximation
type: Item
instance of: scholarly article
title: Wisdom system: dynamics in the adiabatic approximation
zbMATH Open document ID: 1136.70007
author: A. I. V. V. Sidorenko
author: Anatoly Neishtadt
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The authors consider the elliptic planar restricted three-body problem (Sun-Jupiter-asteroid). It is shown that in the leading approximation the Hamiltonian of the problem, averaged over the asteroid and Jupiter mean longitudes near the resonance 3/1, possesses a rather simple structure. Namely, `fast' and `slow' phase variables emerge and, at fixed value of the 'slow' variables, the Hamiltonian becomes identical to that of the mathematical pendulum. This allows the authors to study the qualitative properties of solutions depending on the energy levels. Particularly, in the region of adiabatic chaos they find numerous stable periodic trajectories.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70K70
Mathematics Subject Classification ID: 70H11
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 2139800
zbMATH Keywords: adiabatic chaos
zbMATH Keywords: mean-motion resonances
zbMATH Keywords: mathematical pendulum
MaRDI profile type: Publication
full work available at URL: s10569-004-1008-1
OpenAlex ID: W1977089109
cites work: The elliptic restricted problem at the 3:1 resonance
cites work: Resonant motion in the restricted three-body problem
cites work: Relaxation-chaos phenomena in celestial mechanics. I. On Wisdom's model for the 3/1 Kirkwood gap
cites work: Stable periodic motions in the problem on passage through a separatrix
DOI: 10.1007/S10569-004-1008-1
description: scientific article; zbMATH DE number 2139800