Lateral-Directional Aircraft Dynamics Under Static Moment Nonlinearity

Abstract

T HIS Note specifically focuses on the aircraft lateraldirectional dynamics in the presence of nonlinearity in lateral moments with respect to sideslip (static lateral moments). Such nonlinearity is often encountered during flight in the regimes in which the aerodynamic properties are nonlinear: for example, during high-angle-of-attack flight. In the previous works by the author [1–3], which focus on the multiple-degree-of-freedom wing-rock dynamics at high angles of attack, the results imply that by itself, the nonlinearity in the static lateral moments [such as that considered here (cubic polynomial with respect to sideslip)] does not lead to wing rock. Those analyses, however, consider only the situation in which the nonlinearity is relatively weak. In [4], cubic nonlinearity of static lateral moments with respect to sideslip is shown to cause wing rock in a multimode system in certain conditions. Because of these seemingly discrepant findings, the topic is revisited here. This Note presents detailed analysis of the lateral-directional motion when the cubic type of static lateral moment nonlinearity is present in the system. The equations of motion as derived in [3] are used as the basis for the analysis. To gain physical insight into the problem, an analytical approach using the multiple-time-scales (MTS) method is used (see, for example, [5,6]). Both weak and strong nonlinearity cases are considered.