Free cavitational deceleration of a circular cylinder in a liquid after impact

The problem is considered about the vertical continuous impact and subsequent free deceleration of a circular cylinder semi-immersed in a liquid. The specificity of this problem is that, under certain conditions, some areas of low pressure near the body appear and the attached cavities are formed. The separation zones and the motion law of the cylinder are unknown in advance and have to be determined in solving the problem. The study of the problem is conducted by a direct asymptotic method effective for small spans of time. Some nonlinear problem with unilateral constraints is formulated that is solved together with the equation defining the law of motion of the cylinder. In the case when the space above the external free surface of a liquid is filled with a gas with low pressure (vacuum), an analytical solution of the problem is constructed. To determine the main hydrodynamic characteristics (the separation point and acceleration of the cylinder), we derive a system of transcendental equations with elementary functions. The solution of this system agrees well with the results obtained by the direct numerical method.