Solving procedure for the Kelvin–Kirchhoff equations in case of buoyant (or the falling) ellipsoid of rotation

Abstract

We have presented in this communication a new solving procedure for Kelvin–Kirchhoff equations, considering the dynamics of rising the quasi-rigid ellipsoid of rotation in an ideal incompressible fluid (up to the surface), assuming additionally the dynamical symmetry of rotation for the rising 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 non-rigid ellipsoid rotation has been explored in regard to the existence of an analytic way of presentation for the approximated solution (where we suppose that components of fluid’s torque vector {Ti} are approximately proportional to the appropriate components of angular velocity {Ωi}). The results of calculations for the components of angular velocity {Ωi} should then be used for solving momentum equation of Kelvin–Kirchhoff system. Thus, the full system of equations of Kelvin–Kirchhoff problem has been explored with respect to the existence of an analytic way of presentation of the general solution. The last but not least, we have pointed out the 1-st integral of Kelvin–Kirchhoff system under the aforesaid additional assumption for fluid’s torque vector {Ti} when {Ii} = const (but without the additional restriction of dynamical symmetry onto the form of the rising body, I1=I2).