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., 2014, Volume 19, Issue 3, Pages 187–222 (Mi fpm1594)  

Integrable cases in the dynamics of a multi-dimensional rigid body in a nonconservative field in the presence of a tracking force

M. V. Shamolin

Lomonosov Moscow State University, Moscow, Russia

Abstract: This paper is a survey of integrable cases in the dynamics of a five-dimensional rigid body 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. The problem of the search for complete sets of transcendental first integrals of systems with dissipation is quite topical; a large number of works are devoted to it. We introduce a new class of dynamical systems that have a periodic coordinate. Due to the existence of nontrivial symmetry groups of such systems, we can prove that these systems possess variable dissipation with zero mean, which means that on the average for a period with respect to the periodic coordinate, the dissipation in the system is equal to zero, although in various domains of the phase space, either the energy pumping or dissipation can occur. Based on the facts obtained, we analyze dynamical systems that appear in the dynamics of a five-dimensional rigid body and obtain a series of new cases of complete integrability of the equations of motion in transcendental functions that can be expressed through a finite combination of elementary functions.

Full text: PDF file (270 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2016, 214:6, 865–891

Bibliographic databases:

Document Type: Article
UDC: 517+531.01

Citation: 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”, Fundam. Prikl. Mat., 19:3 (2014), 187–222; J. Math. Sci., 214:6 (2016), 865–891

Citation in format AMSBIB
\Bibitem{Sha14}
\by M.~V.~Shamolin
\paper Integrable cases in the dynamics of a~multi-dimensional rigid body in a~nonconservative field in the presence of a~tracking force
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 3
\pages 187--222
\mathnet{http://mi.mathnet.ru/fpm1594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431882}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 214
\issue 6
\pages 865--891
\crossref{https://doi.org/10.1007/s10958-016-2816-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962323865}


Linking options:
  • http://mi.mathnet.ru/eng/fpm1594
  • http://mi.mathnet.ru/eng/fpm/v19/i3/p187

    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
  • Фундаментальная и прикладная математика
    Number of views:
    This page:225
    Full text:40
    References:16

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