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Fundam. Prikl. Mat., 2010, Volume 16, Issue 4, Pages 3–229 (Mi fpm1332)  

This article is cited in 26 scientific papers (total in 26 papers)

Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems

V. V. Trofimov, M. V. Shamolin

M. V. Lomonosov Moscow State University

Abstract: This paper presents results referred to geometric invariant theory of completely integrable Hamiltonian systems and also to the classification of integrable cases of low-dimensional and high-dimensional rigid body dynamics in a nonconservative force field. The latter problems are described by dynamical systems with variable dissipation. The first part of the work is the base the doctorial dissertation of V. V. Trofimov (1953–2003), which was in parts already published. However, in the present entire form, it was not appeared, and we decided to fill in this gap. The second part is a development of the results presented in the doctorial dissertation of M. V. Shamolin, and it was not appeared in the present variant. These two parts well complement one another, which initiated this work (its sketches already appeared in 1997).

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English version:
Journal of Mathematical Sciences (New York), 2012, 180:4, 365–530

Bibliographic databases:

UDC: 517+531.01

Citation: V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, Fundam. Prikl. Mat., 16:4 (2010), 3–229; J. Math. Sci., 180:4 (2012), 365–530

Citation in format AMSBIB
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\by V.~V.~Trofimov, M.~V.~Shamolin
\paper Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 4
\pages 3--229
\mathnet{http://mi.mathnet.ru/fpm1332}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2786542}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 180
\issue 4
\pages 365--530
\crossref{https://doi.org/10.1007/s10958-012-0650-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855824732}


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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. M. V. Shamolin, “Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force”, J. Math. Sci., 214:6 (2016), 865–891  mathnet  crossref  mathscinet
    2. 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
    3. Shamolin M.V., “Dynamical Pendulum-Like Nonconservative Systems”, Applied Non-Linear Dynamical Systems, Springer Proceedings in Mathematics & Statistics, 93, ed. Awrejcewicz J., Springer-Verlag Berlin, 2014, 503–525  crossref  mathscinet  zmath  isi
    4. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika na ploskosti”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 10(132), 91–113  mathnet  elib
    5. Kozlov V.V., “Rational Integrals of Quasi-Homogeneous Dynamical Systems”, Pmm-J. Appl. Math. Mech., 79:3 (2015), 209–216  crossref  mathscinet  isi
    6. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
    7. M. V. Shamolin, “On the problem of free deceleration of a rigid body with the cone front part in a resisting medium”, Math. Models Comput. Simul., 9:2 (2017), 232–247  mathnet  crossref  zmath  elib
    8. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v trekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2016, no. 3-4, 75–97  mathnet  elib
    9. 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
    10. M. V. Shamolin, “Sluchai integriruemosti, sootvetstvuyuschie dvizheniyu mayatnika v chetyrekhmernom prostranstve”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 1, 41–58  mathnet  elib
    11. 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
    12. 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
    13. 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
    14. M. V. Shamolin, “Integriruemye sistemy s dissipatsiei na kasatelnykh rassloeniyakh k sferam razmernostei $2$$3$”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 145, VINITI RAN, M., 2018, 86–94  mathnet  mathscinet
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. M. V. Shamolin, “Integrable dynamical systems with dissipation on tangent bundles of 2D and 3D manifolds”, J. Math. Sci. (N. Y.), 244:2 (2020), 335–355  mathnet  crossref  elib
    21. Shamolin M.V., “New Cases of Integrable Ninth-Order Systems With Dissipation”, Dokl. Phys., 64:12 (2019)  crossref  isi  scopus
    22. Shamolin V M., “New Cases of Integrable Seventh-Order Systems With Dissipation”, Dokl. Phys., 64:8 (2019), 330–334  crossref  isi  scopus
    23. Shamolin M.V., “New Cases of Integrable Fifth-Order Systems With Dissipation”, Dokl. Phys., 64:4 (2019), 189–192  crossref  isi  scopus
    24. M. V. Shamolin, “Nekotorye integriruemye dinamicheskie sistemy nechetnogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 52–69  mathnet  crossref
    25. 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
    26. M. V. Shamolin, “Dvizhenie tverdogo tela s perednim konusom v soprotivlyayuscheisya srede: kachestvennyi analiz i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 83–108  mathnet  crossref
  • Фундаментальная и прикладная математика
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