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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(1):93-96; doi:10.1093/qjmam/5.1.93
© 1952 by Oxford University Press
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NOTE ON A GENERALIZATION OF RAYLEIGH'S PRINCIPLE

W. J. DUNCAN

( Department of Aeronautics and Fluid Mechanics, The University Glasgow )

Any root {lambda} of the characteristic equation of a set of n linear ordinary differential equations with constant coefficients and of order m is also a root of an equation of degree m whose coefficients are quadratic forms in the modal coordinates corresponding to {lambda}. It is shown that, when the matrices of the coefficients of each order in the differential equations are symmetric, the root {lambda} of the equation of mth degree is stationary for small deviations of the modal coordinates from their true ratios for the mode considered.


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