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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2013, Volume 125, Pages 3–251 (Mi into147)  

This article is cited in 17 scientific papers (total in 17 papers)

Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: This paper is a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00020_


Full text: PDF file (1333 kB)

English version:
Journal of Mathematical Sciences (New York), 2015, 204:4, 379–530

UDC: 517.9+531.01+531.552

Citation: M. V. Shamolin, “Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields”, Dynamical systems, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 125, VINITI, Moscow, 2013, 3–251; J. Math. Sci. (N. Y.), 204:4 (2015), 379–530

Citation in format AMSBIB
\Bibitem{Sha13}
\by M.~V.~Shamolin
\paper Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields
\inbook Dynamical systems
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2013
\vol 125
\pages 3--251
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into147}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 4
\pages 379--530
\crossref{https://doi.org/10.1007/s10958-014-2209-0}


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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. Andreev, M. V. Shamolin, “Matematicheskoe modelirovanie vozdeistviya sredy na tverdoe telo i novoe dvukhparametricheskoe semeistvo fazovykh portretov”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 10(121), 109–115  mathnet
    2. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika na ploskosti”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 10(132), 91–113  mathnet  elib
    3. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v trekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2016, no. 3-4, 75–97  mathnet  elib
    4. M. V. Shamolin, “Integrable systems in dynamics on a tangent foliation to a sphere”, Moscow University Mechanics Bulletin, 71:2 (2016), 27–32  mathnet  crossref  isi  elib
    5. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v chetyrekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 41–58  mathnet  elib
    6. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 1. Dinamicheskie sistemy”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 41–64  mathnet  crossref  elib
    7. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 2. Nezavisimost polya sil ot tenzora uglovoi skorosti”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 4, 40–67  mathnet  crossref  elib
    8. M. V. Shamolin, “A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere”, Moscow University Mechanics Bulletin, 73:3 (2018), 51–59  mathnet  crossref  zmath  isi
    9. M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 3. Zavisimost polya sil ot tenzora uglovoi skorosti”, Vestn. SamU. Estestvennonauchn. ser., 24:2 (2018), 33–54  mathnet  crossref  elib
    10. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernoi sfery”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 78–87  mathnet  mathscinet
    11. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii trekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 110–118  mathnet  mathscinet
    12. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii chetyrekhmernogo mnogoobraziya”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 119–129  mathnet  mathscinet
    13. M. V. Shamolin, “Voprosy kachestvennogo analiza v prostranstvennoi dinamike tverdogo tela, vzaimodeistvuyuschego so sredoi”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 130–142  mathnet  mathscinet
    14. M. V. Shamolin, “Family of phase portraits in the spatial dynamics of a rigid body interacting with a resisting medium”, J. Appl. Industr. Math., 13:2 (2019), 327–339  mathnet  crossref  crossref  elib
    15. M. V. Shamolin, “Sistemy s dissipatsiei: otnositelnaya grubost, negrubost razlichnykh stepenei i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 70–82  mathnet  crossref  mathscinet
    16. M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81  mathnet  crossref
    17. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
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