Power expansions of solutions of the equations of motion of a gyrostat

By applying methods of power geometry, we obtain power expansions of solutions of the equations of motion of a heavy gyrostat around a fixed point, under the assumption that the constant vector of the gyrostatic momentum is directed along one of the principal axes of inertia, on which the center of mass of the gyrostat lies. We establish conditions for the existence of power asymptotics of solutions in the cases when the independent variable tends to zero or infinity, construct 22 families of power expansions and analyze their properties.