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

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Computer Algebra in Scientific Computing (CASC 2019)

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

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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.

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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
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  2. Tatiana Titorenko
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Correspondence to Tatiana Titorenko .

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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

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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

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

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