Construction of librational invariant tori in the spin-orbit problem
type: Item
instance of: scholarly article
title: Construction of librational invariant tori in the spin-orbit problem
zbMATH Open document ID: 0799.70005
DOI: 10.1007/BF00942847
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1994-11-10T00:00:00Z
review text: Spin-orbit resonance problems are investigated for the synchronous (1:1) case, using Hamiltonian dynamics. Transformations, Birkhoff's normalization and the application of KAM theory show the existence of librational tori. The two applications studied are the Earth-Moon system and the Saturn-Rhea system. Once again the Earth-Moon mathematical stability condition does not meet the physical situation, but in the case of the Saturn-Rhea system the proper trapping tori can be constructed according to the existing physical parameters.
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 513157
zbMATH Keywords: Birkhoff's normalization
zbMATH Keywords: KAM theory
zbMATH Keywords: Earth-Moon system
zbMATH Keywords: Saturn-Rhea system
zbMATH Keywords: resonance
zbMATH Keywords: existence
author: Alessandra Celletti
reviewed by: Victor Szebehely
MaRDI profile type: Publication
cites work: PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
cites work: The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
cites work: Analysis of resonances in the spin-orbit problem in celestial mechanics. I: The synchronous resonance
cites work: Analysis of resonances in the spin-orbit problem in celestial mechanics. II: Higher order resonances and some numerical experiments
cites work: Rigorous estimates for a computer-assisted KAM theory
cites work: Construction of analytic KAM-surfaces and effective stability bounds
cites work: Q4763554
cites work: Q3776700
cites work: On the numerical optimization of KAM estimates by classical perturbation theory
cites work: Computer methods and Borel summability applied to Feigenbaum's equation
cites work: Q3657476
cites work: Q5829223
cites work: Computer-assisted proofs in analysis
cites work: Q3294369
full work available at URL: https://doi.org/10.1007/bf00942847
OpenAlex ID: W2082462969
description: scientific article; zbMATH DE number 513157