A kinematic interpretation of the motion of a heavy rigid body with a fixed point

A kinematic interpretation of the motion of a rigid body with a fixed point is proposed using the rolling of a mobile hodograph, which describes, on the ellipsoid of inertia, a vector collinear with the vector of the angular velocity of the body, with respect to a fixed vector. On the basis of this, an interpretation of the motion of the body in the Steklov, Grioli, Dokshevich and Bobylev – Steklov solutions is obtained. A new formula is derived indicating the connection between the angle of precession and the polar angle of the equations of the fixed hodograph, indicated by Kharlamov.