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



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 3, Pages 373–394 (Mi vuu645)  

This article is cited in 1 scientific paper (total in 1 paper)

MECHANICS

On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders

A. I. Safonova, O. V. Kholostovabc

a Research and Production Company “Infosystem-35”, ul. Tret'ya Mytishchinskaya, 16, bld. 37, Moscow, 129626, Russia
b Moscow Aviation Institute (National Research University), Volokolamskoe shosse, 4, Moscow, 125993, Russia
c Moscow Institute of Physics and Technology (State University), Institutskii per., 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: The motion of a near-autonomous time-periodic two-degree-of-freedom Hamiltonian system in the vicinity of a linearly stable trivial equilibrium is considered. The values of the problem parameters are supposed to be such that the system implements both a double combinational third-order resonance and a fourth-order resonance. The problem of existence and stability of resonant periodic motions of the system is considered. The study is carried out using as an example the problem of the motion of a dynamically symmetric satellite (a rigid body) relative to the center of mass in the central Newtonian gravitational field in an elliptical orbit with small eccentricity. The satellite's periodic motions generated from its stationary rotations in a circular orbit (hyperboloidal and conical precessions) for the resonant values of the parameters are considered as unperturbed ones. The normalization of the Hamiltonian functions of perturbed motion is performed, and the equilibrium positions of approximate (model) systems are determined. The corresponding resonant periodic motions of the satellite in the vicinity of these unperturbed motions are obtained by the Poincare method, and their geometric interpretation is given. The unstable periodic motions and the motions that are stable for the majority (in the sense of Lebesgue measure) of the initial conditions and formally stable are revealed.

Keywords: Hamiltonian system, multiple resonance, stability, periodic motion, dynamically symmetrical satellite, hyperboloidal precession, conical precession.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 3.3858.2017/4.6
This work was carried out within the state assignment (project no. 3.3858.2017/4.6).


DOI: https://doi.org/10.20537/vm180308

Full text: PDF file (318 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 531.36
MSC: 70H05, 70H14, 70H15, 70K45
Received: 15.08.2018

Citation: A. I. Safonov, O. V. Kholostova, “On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:3 (2018), 373–394

Citation in format AMSBIB
\Bibitem{SafKho18}
\by A.~I.~Safonov, O.~V.~Kholostova
\paper On periodic motions of a symmetrical satellite in an orbit with small eccentricity in the case of multiple combinational resonance of the third and fourth orders
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 3
\pages 373--394
\mathnet{http://mi.mathnet.ru/vuu645}
\crossref{https://doi.org/10.20537/vm180308}
\elib{http://elibrary.ru/item.asp?id=35645988}


Linking options:
  • http://mi.mathnet.ru/eng/vuu645
  • http://mi.mathnet.ru/eng/vuu/v28/i3/p373

    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. O. V. Kholostova, “O kratnykh rezonansakh chetvertogo poryadka v neavtonomnoi gamiltonovoi sisteme s dvumya stepenyami svobody”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 275–294  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:128
    Full text:81
    References:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020