System approach to calculation of the optimal shape for the wing with ground effect by means of the rayleigh-ritz method

The article deals with the problem of increasing stabilization of an aircraft moving in a stationary flow at an extremely small standoff distance from the interface of media of different densities. This problem can be solved in various ways, one of which is aerodynamic stabilization, implying selection of the special geometry for the bearing surfaces and their configurations. The article describes a system of terms and classical methods for solving problems of optimal bearing surface theory, which is characterized by the fact, that most extreme problems can be classified as ill-posed extremal problems of variational calculus. Their ill-posedness is caused by the fact that the number boundary conditions imposed on the extremal, exceeds the degree of differential equation of the differential equations of the necessary extremum condition. Particular attention is paid to numerical methods for solving optimization problems, in which, using the necessary optimality conditions the problem reduces to finding the minimum of many variables function. We have described in detail the Rayleigh-Ritz method, which is a special case of the method of testing functions. The results of the Rayleigh-Ritz method application to the optimization problem are presented.