NOTE ON A GENERALIZATION OF RAYLEIGH'S PRINCIPLE

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Abstract
Any root λ 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 λ. It is shown that, when the matrices of the coefficients of each order in the differential equations are symmetric, the root λ 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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