Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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



Rus. J. Nonlin. Dyn.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2017, Volume 13, Number 4, Pages 505–518 (Mi nd581)  

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

On the 75th birthday of A.P.Markeev

On spacial motions of an orbital tethered system

A. V. Rodnikova, P. S. Krasil'nikovb

a Bauman Moscow State Technical University, ul. 2-nd Baumanskaya 5, Moscow, 105005, Russia
b Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia

Abstract: We study motions of a particle along a rope with ends fixed to an extended rigid body whose center of mass traces out a circular orbit in the central Newtonian force field. (Such a rope is called a tether.) We assume that the tether realizes an ideal unilateral constraint. We derive particle motion equations on the surface of the ellipsoid, which restricts the particle motion, and conditions that guarantee such motions. We also study the existence and stability of relative equilibria of the particle with respect to the orbital frame of reference. We prove stability of the integral manifold of the particle motions in the plane of the orbit. We note that small-amplitude librations near this manifold can be described by approximate equations that can be reduced to Riccatis equation. We establish that generally the spacial motions of the particle are chaotic for initial conditions from some vicinity of the separatrix motion in the plane of the orbit and are regular in other cases. We also note that chaotic motions usually lead to a situation where the particle comes off the constraint, in other words, to motions inside the above-mentioned ellipsoid.

Keywords: space tethered system, unilateral constraint, tether, chaos, Riccati equation

Funding Agency Grant Number
Russian Science Foundation 14-21-00068


DOI: https://doi.org/10.20537/nd1704004

Full text: PDF file (4162 kB)
References: PDF file   HTML file

UDC: 531.352:629.7
MSC: 37N05, 70F15, 70F20, 70K55
Received: 30.09.2017
Accepted:13.10.2017

Citation: A. V. Rodnikov, P. S. Krasil'nikov, “On spacial motions of an orbital tethered system”, Nelin. Dinam., 13:4 (2017), 505–518

Citation in format AMSBIB
\Bibitem{RodKra17}
\by A.~V.~Rodnikov, P.~S.~Krasil'nikov
\paper On spacial motions of an orbital tethered system
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 4
\pages 505--518
\mathnet{http://mi.mathnet.ru/nd581}
\crossref{https://doi.org/10.20537/nd1704004}
\elib{https://elibrary.ru/item.asp?id=30780697}


Linking options:
  • http://mi.mathnet.ru/eng/nd581
  • http://mi.mathnet.ru/eng/nd/v13/i4/p505

    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. A. P. Deriglazov, A. A. Tikhonov, “The effect of the nonuniformity of the earth's magnetic field on electrodynamic space tether system dynamics”, Vestn. St Petersb. Univ.-Math., 53:3 (2020), 366–375  crossref  mathscinet  zmath  isi  scopus
  • Number of views:
    This page:105
    Full text:46
    References:16

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021