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On Invariant Manifolds and Their Stability in the Problem of Motion of a Rigid Body under the Influence of Two Force Fields

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Computer Algebra in Scientific Computing (CASC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

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Abstract

On the basis of the Routh–Lyapunov method and its generalizations, we study the structure of the phase space of the conservative system which describes the motion of a rigid body in gravitational and magnetic fields. Within the framework of this study, the invariant manifolds of various dimension have been found, their simplest classification has been performed, and sufficient conditions of stability have been obtained for the stationary invariant manifolds.

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References

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Authors and Affiliations

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

    Valentin Irtegov & Tatiana Titorenko

Authors
  1. Valentin Irtegov
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  2. Tatiana Titorenko
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Corresponding author

Correspondence to Valentin Irtegov .

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Hessen, Germany

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Irtegov, V., Titorenko, T. (2015). On Invariant Manifolds and Their Stability in the Problem of Motion of a Rigid Body under the Influence of Two Force Fields. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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