semi-analytical ansatz for approximating dynamics of asteroid rotation approaching planet

The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation approaching planet, in view of future approach apophis 2029 to earth. as previously noted, various perturbations (collisions, close encounters, yorp effect) may destabilize the rotation of minor celestial body (asteroid), deviating it from the current spin-state. we consider here semi-analytical algorithm for calculating regimes of asteroid rotation assuming its being not rubble-pile, but preferably of rigid state of its surface (this would assume almost constant main moments of inertia for asteroid, as first approximation). main euler equations stemming from assumption of conservation of angular momentum have been presented using applied gravitational torques during approach asteroid to planet. new method for solving euler's equations for rigid body rotation is introduced herein; an elegant example of evolution of non-linear spin dynamical state is demonstrated along with semi-analytical findings of kinematic presentation of sequent rotation stages via euler (or wisdom) angles.