  The main motivation of this research is the analytical exploration of the
dynamics of asteroid rotation when it moves in elliptic orbit through Space.
According to the results of Efroimsky, Frouard (2016), various perturbations
(collisions, close encounters, YORP effect) destabilize the rotation of a small
body (asteroid), deviating it from the initial-current spin state. This yields
evolution of the spin towards rotation about maximal-inertia axis due to the
process of nutation relaxation or to the proper spin state corresponding to
minimal energy with a fixed angular momentum. We consider in our research the
aforementioned spin state of asteroid but additionally under non-vanishing
influence of the effects of non-gravitational nature (YORP effect), which is
destabilizing the asteroid rotation during its motion far from giant planets.
Meanwhile, new solutions for asteroid rotation dynamics in case of negligible
(time-dependent) applied torques have been obtained in our development. New
method for solving Euler equations for rigid body rotation is suggested; an
elegant example for evolution of spin towards the rotation about
maximal-inertia axis is calculated.
