A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed point

摘要

A new approach is developed here for resolving of the Poisson equations incase the components of angular velocity of rigid body rotation could beconsidered as the functions of time-parameter t only. Fundamental solution ispresented by the analytical formulae in dependence on two time-dependent, thereal-valued coefficients. Such coefficients as above are proved to be thesolutions of mutual system of 2 Riccati ordinary differential equations (whichhas no analytical solution in general case). All in all, the cases ofanalytical resolving of Poisson equation are quite rare (according to the casesof exact resolving of the aforementioned system of Riccati ODEs). So, thesystem of Euler-Poisson equations is proved to have the analytical solutions(in quadratures) only in classical simplifying cases: 1) Lagrange case, or 2)Kovalevskaya case or 3) Euler case or other well-known but particular cases(where the existence of particular solutions depends on the choosing of theappropriate initial conditions).