The application of perturbation methods to nonlinear problems in flight mechanics

Abstract

Analytical-techniques are developed for deriving approximate solutions to a class of problems that arise in nonlinear flight mechanics typically when an aeroplane is flying close to a stability boundary. The techniques are based on pertoz-bation methods and the method of multiple scales is used to correct for_nonuriformities otherwise present in the asymptotic expai!,. 3ions. Applications are mainly concerned with the lateral dynamics of slender aircraft flying at high incidence. Approximations are derived for both linear and nonlinear lateral motions that serve to illustrate the importance of particular parameters in the problem. For the linear theory the approximations are achieved by reducing the fourth order system to two. weakly coupled second order systems. The nonlinear theory is mainly concerned with the effect of aerodynamic nonlinearity on the lateral oscillation when the latter has marginal stability or instability, as predicted by the linear theory. The analytic approximations are extended for use in the problem of estimating damping moments on aircraft in oscillatory motion. For this purpose approximations are constructed for the logarithmic decrement of a nonlinear oscillation that can be used to fit experimental measurements. Some thoughtis given to-the issue of memory effects in the representation of aerodynamic forces and moments.