Bi-variate partial fractions and their applications to flutter and stability problems

Abstract

A simple expansion method, based on partial fractions of a special type, is described for the construction of bi-variate polynomials of interpolation. A distinctive feature is the choice of a system of straight lines, no three of which are concurrent, in order to define the points for interpolation. The expansion formula, which contains considerably fewer terms than others in general use, can be extended to more variables. The applications considered relate to the expansion and solution of determinantal equations of a type frequently encountered in investigations on the flutter and stability of aeroplanes. Reference is made to the possible use of a d.c. network analyser, based on an electrical interpretation of the expansion formulae, as an aid to rapid solution.