Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field

We present complete results devoted to the study of the equations of motion of a dynamically symmetric four-dimensional rigid body in a nonconservative force field. The form of the body is taken from the dynamics of real two- or three-dimensional rigid bodies interacting with a resisting medium according to the streamline flow around laws under which a non-conservative pair of forces acts on the body and forces the body center of mass to move rectilinearly and uniformly.