A rigid body motion at specified integrals

The paper deals with the problem of finding approximate analytical characteristics of an axially symmetric perfectly rigid body's rotation around a fixed pole in a uniform stationary gravitational field. The body motion is initially set by an involutive system of independent algebraic first integrals in an open connected domain of phase space. The explicit expressions for Euler angles were found, also the geometry of the body movement was determined and the existence condition for its regular precession was obtained.