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On stability boundary of linear multi-parameter Hamiltonian systems

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Abstract

In this paper an approximate equation is derived to describe smooth parts of the stability boundary for linear Hamiltonian systems, depending on arbitrary number of parameters. With this equation, we can obtain parameters corresponding to the stability boundary, as well as to the stability and instability domains, provided that one point on the stability boundary is known. Then differential equations describing the evolution of eigenvalues and eigenvectors along a curve on the stability boundary surface are derived. These equations also allow us to obtain curves belonging to the stability boundary. Applications to linear gyroscopic systems are considered and studied with examples.

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Authors and Affiliations

  1. State Key Laboratory of Structure and Industrial Equipments, Department of Engineering Mechanics, Dalian University of Technology, 116023, Dalian, China

    Qi Zhaohui

  2. Institute of Mechanics, Moscow State Lomonosov University, 117192, Moscow, Russia

    Alexander P. Seyranian

Authors
  1. Qi Zhaohui
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  2. Alexander P. Seyranian
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The project supported by the National Science Foundations of Russia and China (10072012)

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Zhaohui, Q., Seyranian, A.P. On stability boundary of linear multi-parameter Hamiltonian systems. Acta Mech Sinica 18, 661–670 (2002). https://doi.org/10.1007/BF02487969

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  • DOI: https://doi.org/10.1007/BF02487969

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