Stability analysis for time-varying WIG craft dynamics in the presence of wavy boundary and gust

Wing-In-Ground (WIG) crafts are special vehicles that operate under particular situation named ground effect. The stability of WIGs in normal situation of ground effect without presence of disturbance is an LTI problem for cruise condition. Wavy surface and gust are undesired conditions which change aerodynamics and stability derivatives of WIGs. Therefore, the WIG dynamics will be time-varying due to wave and gust characteristics. In this article, a fundamental framework is constructed for analytical analysis of WIGs in the presence of disturbance. To meet this aim, the lift and moment coefficients of a WIG according to wave and gust are computed analytically and time-varying dynamics for the vehicle is derived. Since the speed of waves and gust are assumed to be smaller compared to velocity of the vehicle, slowly time-varying method would be an appropriate approach to justify the stability conditions. Consequently, the necessary conditions for longitudinal dynamic stability are addressed via slowly time-varying analysis which is based on norm of system matrix, norm of its derivative and its eigenvalues for all times. Finally, in order to show the effectiveness of the proposed approach, stability analysis of a 20-passenger WIG at different wave and gust specification are illustrated separately and collectively.