SUMMARY
Two-step hybrid asymptotic method based on perturbation methods and phase integrals (methodWKB) is used to obtain approximate analytical solutions of the nonlinear problem of the vibrations ofthe aircraft near the rough surface, which reduces the need for the integration of singular nonlinear differentialequation with time-variable periodic coefficients for given initial conditions. This solution is notlimited to the value of the dimensionless amplitude of perturbations and the nature of the order non-linearrestoring force. The resulting solution has the form of the sum, where each term consists of two functionsaccording to the method of perturbation (in scalar parameter when the nonlinear component of the originalequation) and the WKB-approximation, effective in the integration of singular differential equations withvariable coefficients. For specific numerical results, a comparison with the data of direct numerical integrationof the equations of the original problem