The problem of takeoff and landing of a hereditarily deformable aircraft in a turbulent atmosphere

The solution to the problem of the movement of an aircraft along the runway in a turbulent atmosphere is a complex and urgent problem. The complexity of the problem lies in the fact that, in the general case, the mathematical model of the problem is reduced to solving nonlinear differential equations, the right side of which is a random function caused by the presence of a turbulent atmosphere. To solve this problem, simplified models of the problem are used, and linear differential equations describe it. If the plane is an inherently deformable solid, then the problem is mathematically described with weakly singular integrodifferential equations with given initial conditions. The present work is devoted to the solution of such problems. In this paper, using the method of eliminating the features of integral and integrodifferential equations, an algorithm for the numerical solution of weight functions has been developed, which allows, in particular, to obtain numerical solutions to the problem when an airplane is considered an ideally elastic solid. Consequently, the algorithm and method of solving the proposed in this paper allow you to test the accuracy of the solution by comparing it with well-known solutions.