Skip to main content
SpringerLink
Log in

On Linear Invariant Manifolds in the Generalized Problem of Motion of a Top in a Magnetic Field

  • Conference paper
  • First Online:
Computer Algebra in Scientific Computing (CASC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

Included in the following conference series:

Abstract

Differential equations describing the rotation of a rigid body with a fixed point under the influence of forces generated by the Barnett–London effect are analyzed. They are a multiparametric system of equations. A technique for finding their linear invariant manifolds is proposed. With this technique, we find the linear invariant manifolds of codimension 1 and use them in the qualitative analysis of the equations. Computer algebra tools are applied to obtain the invariant manifolds and to analyze the equations. These tools proved to be essential.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barnett, S.J.: Magnetization by rotation. Phys. Rev. 6(4), 239–270 (1915)

    Article  Google Scholar 

  2. Egarmin, I.E.: On the magnetic field of a rotating superconducting body. In: Aerophysics and Geocosmic Research. Izd. MOTI, Moscow, pp. 95–96 (1983). (in Russian)

    Google Scholar 

  3. Everitt, C.W.F., et al.: Gravity probe B: final results of a space experiment to test general relativity. Phys. Rev. Lett. 106, 221101 (2011)

    Article  Google Scholar 

  4. Urman, Y.M.: Influence of the Barnett-London effect on the motion of a superconducting rotor in a nonuniform magnetic field. Tech. Phys. 43(8), 885–889 (1998)

    Article  Google Scholar 

  5. Samsonov, V.A.: On the rotation of a rigid body in a magnetic field. Izv. Akad. Nauk SSSR. Mekhanika Tverdogo Tela. 4, 32–34 (1984). (in Russian)

    Google Scholar 

  6. Kozlov, V.V.: To the problem of the rotation of a rigid body in a magnetic field. Izv. Akad. Nauk SSSR. Mekhanika Tverdogo Tela. 6, 28–33 (1985). (in Russian)

    Google Scholar 

  7. Gorr, G.V.: A linear invariant relation in the problem of the motion of a gyrostat in a magnetic field. J. Appl. Math. Meth. 61(4), 549–552 (1997)

    MathSciNet  Google Scholar 

  8. Hess, W.: Über die Euler’schen Bewegungsgleichungen und über eine neue partikuläre Lösung des Problems der Bewegung eines starren Körpers um einen festen Punkt. Math. Ann. 37(2), 153–181 (1890)

    Article  MathSciNet  Google Scholar 

  9. Irtegov, V., Titorenko, T.: On stationary motions of the generalized kowalewski gyrostat and their stability. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2017. LNCS, vol. 10490, pp. 210–224. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66320-3_16

    Chapter  Google Scholar 

  10. Lyapunov, A.M.: On permanent helical motions of a rigid body in fluid. Collected Works, USSR Acad. Sci., Moscow-Leningrad. 1, 276–319 (1954). (in Russian)

    Google Scholar 

  11. Banshchikov, A.V., Burlakova, L.A., Irtegov, V.D., Titorenko, T.N.: Software package for finding and stability analysis of stationary sets. Certificate of State Registration of Software Programs. FGU-FIPS. No. 2011615235 (2011)

    Google Scholar 

  12. Lyapunov, A.M.: The General Problem of the Stability of Motion. Taylor & Francis, London (1992)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for System Dynamics and Control Theory SB RAS, 134, Lermontov street, Irkutsk, 664033, Russia

    Valentin Irtegov & Tatiana Titorenko

Authors
  1. Valentin Irtegov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tatiana Titorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatiana Titorenko .

Editor information

Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Irtegov, V., Titorenko, T. (2019). On Linear Invariant Manifolds in the Generalized Problem of Motion of a Top in a Magnetic Field. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26831-2_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation