Stability of aircraft motion in critical cases

Abstract

Methods developed and/or adapted by Malkin for the analysis of the stability of equilibrium points of autonomous, nonlinear dynamic systems in certain cases are described. The cases are those in which the associated linear system obtained by an expansion about the equilibrium point has either one zero eigenvalue or a pair of pure imaginary eigenvalues, and its remaining eigenvalues have negative real parts. Application of the methods results in either a single nonlinear, autonomous, ordinary, differential equation or a pair of such equations which describe the motion in the critical mode. Two simple examples are presented. The methods are then applied to determine the stability of the motion of a rapidly rolling aircraft in the case of one zero eigenvalue and of an aircraft flying at a relatively high angle of attack when the associated linear system has a pair of pure imaginary eigenvalues.