We can study the motions of an asymmetrical rigid body, submitted to no-power forces (e. g., Coriolis's or Lorentz's forces), with respect to a point O. The dynamical problem is reduced to integration for a subset of $\infty^{4}$ motions; which, as particular cases, includes some motions already known. We can, finally, determine a motion which asymptotically is to become a permanent rotation around a principal axis of inertia; which in its turn is to assume a privileged direction.