RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2017, Volume 22, Issue 1, Pages 54–77 (Mi rcd243)  

This article is cited in 4 scientific papers (total in 4 papers)

Secular Dynamics of a Planar Model of the Sun-Jupiter-Saturn-Uranus System; Effective Stability in the Light of Kolmogorov and Nekhoroshev Theories

Antonio Giorgillia, Ugo Locatellib, Marco Sansotteraa

a Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, 20133, Milano, Italy
b Dipartimento di Matematica, Università degli Studi di Roma ''Tor Vergata'', via della Ricerca Scientifica 1, 00133, Roma, Italy

Abstract: We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, which can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that underlies the analytic part of Nekhoroshev’s theorem to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.

Keywords: $n$-body planetary problem, KAM theory, Nekhoroshev theory, normal form methods, exponential stability, Hamiltonian systems, celestial mechanics

Funding Agency Grant Number
Italian Ministry of Education, University and Research PRIN 2010JJ4KPA009
This work has been supported by the research program “Teorie geometriche e analitiche dei sistemi Hamiltoniani in dimensioni finite e infinite”, PRIN 2010JJ4KPA009, financed by MIUR.


DOI: https://doi.org/10.1134/S156035471701004X

References: PDF file   HTML file

Bibliographic databases:

MSC: 70F10, 37J40, 37N05, 70-08, 70H08
Received: 03.10.2016
Accepted:20.12.2016
Language:

Citation: Antonio Giorgilli, Ugo Locatelli, Marco Sansottera, “Secular Dynamics of a Planar Model of the Sun-Jupiter-Saturn-Uranus System; Effective Stability in the Light of Kolmogorov and Nekhoroshev Theories”, Regul. Chaotic Dyn., 22:1 (2017), 54–77

Citation in format AMSBIB
\Bibitem{GioLocSan17}
\by Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
\paper Secular Dynamics of a Planar Model of the Sun-Jupiter-Saturn-Uranus System; Effective Stability in the Light of Kolmogorov and Nekhoroshev Theories
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 1
\pages 54--77
\mathnet{http://mi.mathnet.ru/rcd243}
\crossref{https://doi.org/10.1134/S156035471701004X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000394354800004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85012180658}


Linking options:
  • http://mi.mathnet.ru/eng/rcd243
  • http://mi.mathnet.ru/eng/rcd/v22/i1/p54

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ma D.-Zh., Fu Ya.-N., Wang X.-L., “The Orbital Configuration of the Two Interacting Jupiters in Hd 155358 System”, Mon. Not. Roy. Astron. Soc., 470:1 (2017), 706–712  crossref  isi  scopus
    2. D. Bambusi, A. Fusè, M. Sansottera, “Exponential Stability in the Perturbed Central Force Problem”, Regul. Chaotic Dyn., 23:7-8 (2018), 821–841  mathnet  crossref
    3. F. Paita, A. Celletti, G. Pucacco, “Element history of the Laplace resonance: a dynamical approach”, Astron. Astrophys., 617 (2018), A35  crossref  isi  scopus
    4. M. Volpi, U. Locatelli, M. Sansottera, “A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems”, Celest. Mech. Dyn. Astron., 130:5 (2018), 36  crossref  mathscinet  isi  scopus
  • Number of views:
    This page:72
    References:26

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019