On the Use in Stability Analysis of the Relationships between the Coefficients of a Quartic Equation and those of a Quadratic Factor

摘要

The stability of the perturbed longitudinal motion of an unaugmented aircraft about a given trimmed flight condition is determined by the well-known stability quartic. It is shown that two basic relationships exist between the coefficients of the quartic and those of a quadratic factor. It is possible to use the relationships to derive a further equation connecting the two coefficients of the quadratic factor as a single stability parameter is varied, all others being held constant. Examination of the position of the locus traced out by the point defined by the coefficients of the quadratic in relation to the axes and the parabolic boundary (separating real and complex roots) enables the trends in the nature of and the degree of stability of the mode or modes represented by the quadratic factor to be determined. The use of this (as far as is known, novel) method of analysing aircraft stability is illustrated by a number of examples. (Author)