Abstract:
An approximate analytical method is developed for the solution of a fourth order, non-linear equation of motion from which the frequency and amplitude of a sustained oscillation may be derived. The criterion for the existence of the limit cycle is a modified form of Routh's discriminant, its sign, and the sign of its derivative with respect to the square of the instantaneous amplitude. Comparisons at spot points show excellent agreement with 'exact' digital computations. The method has been applied to the lateral motion limit cycle encountered at low speeds on the HP 115 aircraft, and comparisons with the results of wind tunnel dynamic simulations show that the onset and nature of the sustained oscillation is predicted very satisfactorily.
