Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.