Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics

Luca Biasco; Luigi Chierchia

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 2, page 85-89
  • ISSN: 1120-6330

Abstract

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The classical D’Alembert Hamiltonian model for a rotational oblate planet revolving near a «day-year» resonance around a fixed star on a Keplerian ellipse is considered. Notwithstanding the strong degeneracies of the model, stability results a là Nekhoroshev (i.e. for times which are exponentially long in the perturbative parameters) for the angular momentum of the planet hold.

How to cite

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Biasco, Luca, and Chierchia, Luigi. "Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.2 (2002): 85-89. <http://eudml.org/doc/252415>.

@article{Biasco2002,
abstract = {The classical D’Alembert Hamiltonian model for a rotational oblate planet revolving near a «day-year» resonance around a fixed star on a Keplerian ellipse is considered. Notwithstanding the strong degeneracies of the model, stability results a là Nekhoroshev (i.e. for times which are exponentially long in the perturbative parameters) for the angular momentum of the planet hold.},
author = {Biasco, Luca, Chierchia, Luigi},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {D’Alembert model; Nekhoroshev estimates; Spin-orbit resonances; Exponential stability; D'Alambert model; spin-orbit resonances; exponential stability},
language = {eng},
month = {6},
number = {2},
pages = {85-89},
publisher = {Accademia Nazionale dei Lincei},
title = {Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics},
url = {http://eudml.org/doc/252415},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Biasco, Luca
AU - Chierchia, Luigi
TI - Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/6//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 2
SP - 85
EP - 89
AB - The classical D’Alembert Hamiltonian model for a rotational oblate planet revolving near a «day-year» resonance around a fixed star on a Keplerian ellipse is considered. Notwithstanding the strong degeneracies of the model, stability results a là Nekhoroshev (i.e. for times which are exponentially long in the perturbative parameters) for the angular momentum of the planet hold.
LA - eng
KW - D’Alembert model; Nekhoroshev estimates; Spin-orbit resonances; Exponential stability; D'Alambert model; spin-orbit resonances; exponential stability
UR - http://eudml.org/doc/252415
ER -

References

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  1. V.I. Arnold (ed.), Encyclopaedia of Mathematical Sciences. Dynamical Systems III, Springer-Verlag, 3, 1988. Zbl0623.00023MR923953DOI10.1007/978-3-642-61551-1
  2. Biasco, L. - Chierchia, L., On the stability of some properly-degenerate Hamiltonian systems. Discrete and Continuous Dynamical Systems, series A, to appear. Zbl1032.37039
  3. Biasco, L. - Chierchia, L., Effective Hamiltonian for the D’Alembert planetary model near a spin/orbit resonance. To appear. Zbl1083.70014MR1956525DOI10.1023/A:1020151319725
  4. Biasco, L. - Chierchia, L. - Treschev, D., Total stability of properly-degenerate Hamiltonian systems with two degrees-of-freedom. Preprint 2001. Zbl1095.37027
  5. Chierchia, L. - Gallavotti, G., Drift and diffusion in phase space. Ann. Inst. Henri Poincaré, Phys. Théor., 60, 1994, 1-144. Erratum, Ann. Inst. Henri Poincaré, Phys. Théor., 68, n. 1, 135, 1998. Zbl1010.37039MR1259103
  6. Poincaré, H., Les Méthodes Nouvelles de la Méchanique Céleste. Gauthier Villars, Paris1892. JFM30.0834.08

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