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Application of the Method of Asymptotic Solution to One Multi-Parameter Problem

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Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

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Abstract

We propose software implementation of the method of computation of asymptotic expansions (see [1,2]) of branches of the set of zeros of a polynomial in three variables near a singular point at which this polynomial is annulled with its partial derivatives. We apply this method for investigation of the set of stability of some gyroscopic system with 4 degrees of freedom and with 3 parameters. It is also possible to compute the set of stability with the help of this method for more general system with 5 parameters.

This work was supported by RFBR, Grant No. 11-01-00023.

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References

  1. Bruno, A.D., Batkhin, A.B.: Asymptotic solution of an algebraic equation. Doklady Mathematics 84(2), 634–639 (2011)

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  2. Bruno, A.D., Batkhin, A.B.: Resolution of an algebraic singularity by power geometry algorithms. Programming and Computer Software 38(2), 57–72 (2012)

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  3. Batkhin, A.B., Bruno, A.D., Varin, V.P.: Sets of stability of Mmulti-parameter Hamiltonian problems. J. Appl. Math. and Mech. 76(1), 56–92 (2012)

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  4. Batkhin, A.B.: Stability of Certain Multiparameter Hamiltonian System. Preprint No. 69, Keldysh Inst. Appl. Math., Moscow (2011) (in Russian)

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  5. Malkin, I.G.: Theory of Stability of Motion. U.S. Atomic Energy Commission, Office of Technical Information, Oak Bridge (1958)

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Miusskaya sq. 4, Moscow, 125047, Russia

    Alexander Batkhin

Authors
  1. Alexander Batkhin
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2012 Springer-Verlag Berlin Heidelberg

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Batkhin, A. (2012). Application of the Method of Asymptotic Solution to One Multi-Parameter Problem. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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