If an algebraic polynomial equation has roots which are negative if real and have negative real parts if complex, the coefficients must satisfy certain fundamental conditions originally formulated by Routh. These conditions are here derived by comparatively simple algebra for the sextic equation by a method which can be generalized; its extension to equations of the eighth and tenth degree is indicated. The case of damped Lagrangian frequency equations is considered as an appropriate epilogue.
Morris, J. and Head, J.W. (1954), "A Note on the Escalator Process: Routh's Stability Criteria for Polynomial Characteristic Equations Derived by Algebra", Aircraft Engineering and Aerospace Technology, Vol. 26 No. 11, pp. 388-389. https://doi.org/10.1108/eb032492
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