  We have presented in this communication a new solving procedure for the
dynamics of non-rigid asteroid rotation, considering the final spin state of
rotation for a small celestial body (asteroid). The last condition means the
ultimate absence of the applied external torques (including short-term effect
from torques during collisions, long-term YORP effect, etc.). Fundamental law
of angular momentum conservation has been used for the aforementioned solving
procedure. The system of Euler equations for dynamics of non-rigid asteroid
rotation has been explored with regard to the existence of an analytic way of
presentation of the approximated solution. Despite of various perturbations
(such as collisions, YORP effect) which destabilize the rotation of asteroid
via deviating from the current spin state, the inelastic (mainly, tidal)
dissipation reduces kinetic energy of asteroid. So, evolution of the spinning
asteroid should be resulting by the rotation about maximal-inertia axis with
the proper spin state corresponding to minimal energy with a fixed angular
momentum. Basing on the aforesaid assumption (component K_1 is supposed to be
fluctuating near the given appropriate constant of the fixed angular momentum),
we have obtained that 2-nd component K_2 is the solution of appropriate Riccati
ordinary differential equation of 1-st order, whereas component K_3 should be
determined via expression for K_2.
