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: 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 ${\left | \lambda \right |_{\min }}$ of the eigenvalue for the nonlinear eigenvalue problem of the total system. Estimations of ${\left | \lambda \right |_{\min }}$ are given, and applications of the stability criterion are shown by numerical examples.
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E. I. Jury, Stability tests for one-, two- and multidimensional linear systems, Proc. IEE 124, 1237–1240 (1977)
M. Frik, Zur Stabilität nichtkonservativer linearer Systeme, ZAMM 52, T47–T49 (1972)
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W. Kliem, Zur Stabilität nichtkonservativer Differentialgleichungssysteme, ZAMM 63, 329–331 (1983)
P. Weidner, Zur Stabilität linearer Systeme unter dem Einfluss von Dämpfungs—und Kreiselkräften, ZAMM 50, T249–T250 (1970)
D. M. Smith, The motion of a rotor carried by a flexible shaft in flexible bearings, Proc. Royal Soc. A, 142, 92 (1933)
W. Hauger, Stability of a gyroscopic nonconservative system, J. Appl. Mech. 42, 739–740 (1975)
E. I. Jury, Stability tests for one-, two- and multidimensional linear systems, Proc. IEE 124, 1237–1240 (1977)
M. Frik, Zur Stabilität nichtkonservativer linearer Systeme, ZAMM 52, T47–T49 (1972)
K. Huseyin & R. H. Plaut, Extremum properties of the generalized Rayleigh quotient associated with flutter instability, Quart. Appl. Math. 32, 189–201 (1974)
J. Genin & J. S. Maybee, Nonconservative linear systems with constant coefficients, J. Inst. Math. Applic. 8, 358–370 (1971)
J. A. Walker & W. E. Schmitendorf, A simple test for asymptotic stability in partially dissipative symmetric systems, J. Appl. Mech. 40, 1120–1121 (1973)
I. Fawzy, A simplified stability criterion for nonconservative systems, J. Appl. Mech. 46, 423–426 (1979)
W. Kliem, Zur Stabilität nichtkonservativer Differentialgleichungssysteme, ZAMM 63, 329–331 (1983)
P. Weidner, Zur Stabilität linearer Systeme unter dem Einfluss von Dämpfungs—und Kreiselkräften, ZAMM 50, T249–T250 (1970)
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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Article copyright:
© Copyright 1986
American Mathematical Society
