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Nelin. Dinam., 2011, Volume 7, Number 2, Pages 295–311 (Mi nd260)  

This article is cited in 8 scientific papers (total in 8 papers)

On a particle motion along the leier fixed in a precessing rigid body

A. V. Rodnikov

Bauman Moscow State Technical University

Abstract: We study a particle motion along a cable with ends fixed in a precessed rigid body. Such cable called «the leier» is a model of space elevator for a dynamically symmetric asteroid. (The Dutch term «leier» means the rope with fixed ends). In this paper we find two integrable cases of the particle motion equations (for zero and right nutation angle) Phase portraits for integrable situations are built taking into account conditions of motion with the tense cable and assuming the body gravitation is close to gravitational field of two equal point masses that are in the axis of dynamical symmetry. Using «the Generalized Restricted Circular Problem of Three Bodies» by V. V. Beletsky, we study the particle equilibria on the leier in the plane containing the body mass center and being perpendicular to the precession axis for all possible nutation angles. Some facts on these equilibria stability are formulated.

Keywords: space elevator, space tether system, asteroid, unilateral constraint, problem of three bodies.

Full text: PDF file (683 kB)
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UDC: 531.352:629.7
MSC: 37N05, 70H03, 70H09
Received: 07.06.2011
Revised: 23.06.2011

Citation: A. V. Rodnikov, “On a particle motion along the leier fixed in a precessing rigid body”, Nelin. Dinam., 7:2 (2011), 295–311

Citation in format AMSBIB
\Bibitem{Rod11}
\by A.~V.~Rodnikov
\paper On a particle motion along the leier fixed in a precessing rigid body
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 2
\pages 295--311
\mathnet{http://mi.mathnet.ru/nd260}


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    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. V. Rodnikov, “O komplanarnykh ravnovesiyakh kosmicheskoi stantsii na trose, zakreplennom na pretsessiruyuschem asteroide”, Nelineinaya dinam., 8:2 (2012), 309–322  mathnet
    2. V. V. Beletskii, A. V. Rodnikov, “Tochki libratsii obobschennoi ogranichennoi krugovoi zadachi trekh tel v sluchae mnimogo rasstoyaniya mezhdu prityagivayuschimi tsentrami”, Nelineinaya dinam., 8:5 (2012), 931–940  mathnet
    3. A. V. Rodnikov, “Komplanarnye tochki libratsii obobschennoi ogranichennoi krugovoi zadachi trekh tel v sluchae kompleksno-sopryazhennykh mass prityagivayuschikh tsentrov”, Nelineinaya dinam., 9:4 (2013), 697–710  mathnet
    4. A. V. Rodnikov, “Treugolnye tochki libratsii obobschennoi ogranichennoi krugovoi zadachi trekh tel v sluchae kompleksno-sopryazhennykh mass prityagivayuschikh tsentrov”, Nelineinaya dinam., 10:2 (2014), 213–222  mathnet
    5. A. V. Rodnikov, “Modelirovanie dinamiki kosmicheskoi stantsii v okrestnosti asteroida”, Mat. modelir. i chisl. metody, 2016, no. 10, 55–68  mathnet
    6. A. V. Rodnikov, P. S. Krasilnikov, “O prostranstvennykh dvizheniyakh orbitalnoi leernoi svyazki”, Nelineinaya dinam., 13:4 (2017), 505–518  mathnet  crossref  elib
    7. Rodnikov A.V., Fundamental and Applied Problems of Mechanics - 2017, IOP Conference Series-Materials Science and Engineering, 468, IOP Publishing Ltd, 2018  crossref  isi  scopus
    8. Rodnikov A.V., “On Safe Configurations of a Natural-Artificial Space Tether System”, AIP Conference Proceedings, 1959, ed. Kustova E. Leonov G. Morosov N. Yushkov M. Mekhonoshina M., Amer Inst Physics, 2018, UNSP 040018  crossref  isi  scopus
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