A method for calculating non-stationary flow of an arbitrary profile

The article deals with non-stationary continuous flow of an arbitrary profile fluctuating as a solid with small amplitude under some harmonic law by potential flow of incompressible liquid. We have used the Kutta-Zhukovsky postulate to eliminate the features of a kernel of Fredholm integral equation of the second kind with respect to the value of non-stationary speed at the point of profile trailing edge. The hydrodynamic meaning of the carried-out elimination of the features of a kernel lies in the fact that the decision is sought in the class of functions that ensure the continuity of pressure everywhere in the flow, including the sharp trailing edge. The critical streamline of a stationary flow necessary for calculating improper integrals is defined as a solution to the Cauchy problem. Replacing the integrals in the equations with finite sums, we obtain systems of N algebraic equations with respect to the sought quantities.