QI Zhao-hui, Alexander P. Seyranian. On the Stability Boundary of Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 173-178.
Citation: QI Zhao-hui, Alexander P. Seyranian. On the Stability Boundary of Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2002, 23(2): 173-178.

On the Stability Boundary of Hamiltonian Systems

  • Received Date: 2000-06-22
  • Rev Recd Date: 2001-09-18
  • Publish Date: 2002-02-15
  • The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
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  • [1]
    Vishik M I,Lyusternik L A.Solution of some perturbation problems in the case of matrices and selfadjoint or non-self-adjoint equations[J].Russian Mathematical Surveys,1960,15(3):1-73.
    [2]
    Lancaster P.On eigenvalues of matrices depending on a parameter[J].Numer Math,1964,10(4):377-387.
    [3]
    Sun J G.Eigenvalues and eigenvectors of a matrix dependent on a parameter[J].J Comput Math,1985,3(3):351-364.
    [4]
    Anord V L.Geometrical Methods in the Theory of Ordinary Differential Equations[M].New York:Springer-Verlag,1983.
    [5]
    Seyranian A P.Sensitivity analysis of multiple eigenvalues[J].Mech Struct & Mach,1993,21(2):261-284.
    [6]
    Pedersen P,Seyranian A P.Sensitivity analysis of problems of dynamic stability[J].Int J Solids Structures,1983,19(4):315-335.
    [7]
    Yakubovitch V A,Strzhinskii V M.Parametric Resonance in Linear Systems[M].Moscow:Nauka,1987.
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