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

  • Alexander Batkhin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

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.

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References

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    Bruno, A.D., Batkhin, A.B.: Asymptotic solution of an algebraic equation. Doklady Mathematics 84(2), 634–639 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
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    Bruno, A.D., Batkhin, A.B.: Resolution of an algebraic singularity by power geometry algorithms. Programming and Computer Software 38(2), 57–72 (2012)zbMATHCrossRefGoogle Scholar
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    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)CrossRefGoogle Scholar
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    Batkhin, A.B.: Stability of Certain Multiparameter Hamiltonian System. Preprint No. 69, Keldysh Inst. Appl. Math., Moscow (2011) (in Russian)Google Scholar
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    Malkin, I.G.: Theory of Stability of Motion. U.S. Atomic Energy Commission, Office of Technical Information, Oak Bridge (1958)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Batkhin
    • 1
  1. 1.Keldysh Institute of Applied MathematicsMoscowRussia

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