About analytical ansatz to the solving procedure for Kelvin–Kirchhoff equations

Abstract

Abstract In this paper, absolutely new analytical ansatz for solving Kelvin–Kirchhoff equations has been presented. The aforesaid approach was formulated first in Ershkov (2017) for solving Poisson equations; furthermore, a new type of the solving procedure for Euler–Poissonequations (rigid body rotation over the fixed point) is implemented here for solving momentum equation of Kelvin–Kirchhoff. The system of equations of Kelvin–Kirchhoff problem has been explored with regard to the existence of an analytic way of presentation of the analytical solution. A new and elegant ansatz is suggested in this publication whereby, in solving, the momentum equation is reduced to a system of three linear ODEs of 1st order in regard to the three components of the velocity of the spherical particle (dependent on time t). In this premise, a proper elegant partial solution has been obtained due to the invariant dependence between temporary components of the solution. We conclude that the system of Kelvin–Kirchhoff equations has not the analytical presentation of solution (in quadratures) even in case of zero components of fluid force, influencing on the motion of the particle.