(ВД "Освіта України", 2014) Azarskov, V. N.; Gristchak, D. D.
Two-step hybrid asymptotic method based on perturbation methods and phase integrals (me-
thod WKB) is used to obtain approximate analytical solutions of the nonlinear problem of the vibrations of
the aircraft near the rough surface, which reduces the need for the integration of singular nonlinear dif-
ferential equation with time-variable periodic coefficients for given initial conditions. This solution is not
limited to the value of the dimensionless amplitude of perturbations and the nature of the order non-linear
restoring force. The resulting solution has the form of the sum, where each term consists of two functions
according to the method of perturbation (in scalar parameter when the nonlinear component of the original
equation) and the WKB-approximation, effective in the integration of singular differential equations with
variable coefficients. For specific numerical results, a comparison with the data of direct numerical inte-
gration of the equations of the original problem
