The exact analytical solution of the Euler-Poisson equations and its interpretation

The results on the explicit analytical exact solvability of the classical Euler-Poisson equations for the dynamics of a heavy solid are formulated, including a description of the structure of the general exact solution in the form of a special zeta function (exponent of the zeta function of the canonical parabolic automorphic form of weight 12) and the corresponding analytical zeta functional structure of partial solutions in the class of exponents of the zeta functions of elliptic curves with rational coefficients. Geometric and mechanical interpretations of the formulas of the obtained exact solutions are given; their invariant algebraic structure based on the simple exceptional Lie algebra e_8 is shown and their connection with solutions of classical integrability cases is discussed, highlighting the special role of the most mysterious and analytically complex Kovalevskaya case