Skip to main content
SpringerLink
Log in

New invariant relations for one critical subsystem of a generalized two-field gyrostat

  • Mechanics
  • Published:
Doklady Physics Aims and scope Submit manuscript

An Erratum to this article was published on 01 January 2018

This article has been updated

Abstract

In this paper new invariant relations for one critical subsystem of a completely integrable Hamiltonian system with three degrees of freedom found by V.V. Sokolov and A.V. Tsyganov, known as a generalized two-field gyrostat, are obtained. The dynamic system that is induced on the invariant four-dimensional submanifolds is almost everywhere Hamiltonian with two degrees of freedom. The type of system motions on this invariant manifold is determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Change history

  • 01 March 2018

    The following sentence should be added to the section ACKNOWLEDGMENTS:

  • 01 March 2018

    The following sentence should be added to the section ACKNOWLEDGMENTS:

References

  1. V. V. Sokolov and A. V. Tsyganov, Theor. Math. Phys. 131 (1), 543 (2002).

    Article  Google Scholar 

  2. A. V. Borisov and I. S. Mamaev, Rigid Body Dynamics. Hamiltonian Methods, Integrability, Chaos, Moscow–Izhevsk: Institute of Computer Science, 2005, p. 576.

    MATH  Google Scholar 

  3. P. E. Ryabov, Theor. Math. Phys. 176 (2), 1000 (2013).

    Article  Google Scholar 

  4. O. I. Bogoyavlensky, Communs. Math. Phys. 95, 307 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  5. M. P. Kharlamov, Reg. Chaot. Dyn. 10 (4), 381 (2005).

    Article  Google Scholar 

  6. P. E. Ryabov, J. Geom. Phys. 87, 415 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  7. A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Russ. Math. Surv. 65 (2), 259–318 (2010).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Blagonravov Institute of Machines Science, Russian Academy of Sciences, Moscow, Russia

    S. V. Sokolov

  2. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    S. V. Sokolov

Authors
  1. S. V. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Sokolov.

Additional information

Original Russian Text © S.V. Sokolov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 6, pp. 660–663.

The article was translated by the author.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sokolov, S.V. New invariant relations for one critical subsystem of a generalized two-field gyrostat. Dokl. Phys. 62, 567–570 (2017). https://doi.org/10.1134/S1028335817120096

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335817120096

Search

Navigation