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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2009, Volume 5, Number 1, Pages 53–82 (Mi nd78)  

This article is cited in 4 scientific papers (total in 4 papers)

Multiparticle systems. The algebra of integrals and integrable cases

A. V. Borisovab, A. A. Kilinab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector. A corresponding algebra of integrals constituted by the integrals of momentum, angular momentum, and Galilean momentum is presented. Particle systems with a particle-interaction potential homogeneous of degree $\alpha=-2$ are considered. The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. A new nonlinear algebra of integrals including the Jacobi integral is found. A systematic description is given to a new reduction procedure and possibilities of applying it to dynamics with the aim of lowering the order of Hamiltonian systems.
Some new integrable and superintegrable systems generalizing the classical ones are also described. Certain generalizations of the Lagrangian identity for systems with a particle-interaction potential homogeneous of degree $\alpha=-2$ are presented. In addition, computational experiments are used to prove the nonintegrability of the Jacobi problem on a plane.

Keywords: multiparticle systems, Jacobi integral.

Full text: PDF file (508 kB)

Document Type: Article
MSC: 70Hxx, 70G65
Received: 11.07.2008

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Multiparticle systems. The algebra of integrals and integrable cases”, Nelin. Dinam., 5:1 (2009), 53–82

Citation in format AMSBIB
\Bibitem{BorKilMam09}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Multiparticle systems. The algebra of integrals and integrable cases
\jour Nelin. Dinam.
\yr 2009
\vol 5
\issue 1
\pages 53--82
\mathnet{http://mi.mathnet.ru/nd78}


Linking options:
  • http://mi.mathnet.ru/eng/nd78
  • http://mi.mathnet.ru/eng/nd/v5/i1/p53

    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. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Burov, “On the motion of a solid body on spherical surfaces”, Journal of Mathematical Sciences, 199:5 (2014), 501–509  mathnet  crossref  mathscinet
    3. I. A. Bizyaev, “Ob odnom obobschenii sistem tipa Kalodzhero”, Nelineinaya dinam., 10:2 (2014), 209–212  mathnet
    4. A. V. Borisov, I. S. Mamaev, “Symmetries and reduction in nonholonomic mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref
  • Нелинейная динамика
    Number of views:
    This page:167
    Full text:58
    First page:1

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