Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the stability of linear nonconservative systems

Authors: W. Kliem and Chr. Pommer
Journal: Quart. Appl. Math. 43 (1986), 457-461
MSC: Primary 70J25; Secondary 34D20
DOI: https://doi.org/10.1090/qam/846157
MathSciNet review: 846157
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Abstract | References | Similar Articles | Additional Information

Abstract: For a system of linear second-order differential equations, a stability criterion is derived which gives a simple relation between eigenvalues of two of the coefficient matrices and an estimate of the lower bound $ {\left\vert \lambda \right\vert _{\min }}$ of the eigenvalue for the nonlinear eigenvalue problem of the total system. Estimations of $ {\left\vert \lambda \right\vert _{\min }}$ are given, and applications of the stability criterion are shown by numerical examples.

References [Enhancements On Off] (What's this?)

  • [1] W. Hauger, Stability of a gyroscopic nonconservative system, J. Appl. Mech. 42, 739-740 (1975)
  • [2] E. I. Jury, Stability tests for one-, two- and multidimensional linear systems, Proc. IEE 124, 1237-1240 (1977)
  • [3] M. Frik, Zur Stabilität nichtkonservativer linearer Systeme, ZAMM 52, T47-T49 (1972)
  • [4] K. Huseyin & R. H. Plaut, Extremum properties of the generalized Rayleigh quotient associated with flutter instability, Quart. Appl. Math. 32, 189-201 (1974) MR 0430427
  • [5] J. Genin & J. S. Maybee, Nonconservative linear systems with constant coefficients, J. Inst. Math. Applic. 8, 358-370 (1971) MR 0296416
  • [6] J. A. Walker & W. E. Schmitendorf, A simple test for asymptotic stability in partially dissipative symmetric systems, J. Appl. Mech. 40, 1120-1121 (1973) MR 0421792
  • [7] I. Fawzy, A simplified stability criterion for nonconservative systems, J. Appl. Mech. 46, 423-426 (1979) MR 533352
  • [8] W. Kliem, Zur Stabilität nichtkonservativer Differentialgleichungssysteme, ZAMM 63, 329-331 (1983)
  • [9] P. Weidner, Zur Stabilität linearer Systeme unter dem Einfluss von Dämpfungs--und Kreiselkräften, ZAMM 50, T249-T250 (1970)
  • [10] D. M. Smith, The motion of a rotor carried by a flexible shaft in flexible bearings, Proc. Royal Soc. A, 142, 92 (1933)

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DOI: https://doi.org/10.1090/qam/846157
Article copyright: © Copyright 1986 American Mathematical Society

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