The work is devoted to the study of the influence of elastic and viscous properties of a body similar in shape to a ball on its free angular movements. In the presented problems, taking into account body deformations is fundamental, because leads to a qualitative restructuring of its dynamics. Using the example of a specific system, we consider the possibility of significant movement of the axis of stationary rotation to a new position in the body (global movement of the pole) with a small change in the angular velocity of rotation of the body. The change in the position of the axis is described geometrically. In the conservative case, using the integral of energy and the integral of the square of the kinetic momentum vector, the polodes (the trajectories of movement of the kinetic momentum vector relative to the body) are depicted. In the problem of nutation of a quasi-ball, it is shown that the periods of nutation of a body, with and without taking into account its elastic and viscous properties, can differ significantly. The idea of these effects of rigid body dynamics can be useful when considering the movement of the Earth's poles and its Chandler nutation.