RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


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

This article is cited in 13 scientific papers (total in 13 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).

Full text: PDF file (1615 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
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
\Bibitem{TroSha10}
\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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855824732}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1332
  • http://mi.mathnet.ru/eng/fpm/v16/i4/p3

    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. 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
  • Фундаментальная и прикладная математика
    Number of views:
    This page:543
    Full text:199
    References:32
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019