Solving procedure for the Kelvin–Kirchhoff equations in case of non-stationary rotations of slim disc

Abstract

We have presented in this communication a new solving procedure for Kelvin–Kirchhoff equations, considering the dynamics of the falling or ascending the rigid disc in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation for the falling or ascending body, I1 = I2. Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of disc’s rotation has been explored in regard to the existence of an analytic way of presentation for the approximated solution (where we consider the case of laminar flow at slow regime of deceleration of the symmetric disc’s rotation). This scenario is associated with consideration of that the Stokes boundary layer phenomenon on the boundaries of the body has also been assumed at formulation of basic Kelvin-Kirchhoff equations. It allows us to use the results of Jeffery’s fundamental work, in which analytical solution for rotations of spheroid’s particle in Euler angles was obtained. The results of calculations for the components of angular velocity {Ωi} should then be used for solving momentum equation of Kelvin–Kirchhoff system.