FREE EULER MOTION OF TRIAXIAL RIGID EARTH
三轴刚性地球体的自由Euler运动

Under the assumption that the Earth is a triaxial rigid body which is rotating freely in the Euclidian space, the elliptic integral solution of the Euler dynamic equation is provided, and then the numerical solutions of the Euler dynamic as well as kinetic equation are realized. The calculated results show that, besides the self-rotation of the Earth with the period about 24 h and the free Euler precession with the period 305 d, there exists a free nutation with the period about 305 d. In addition, the three Eulerian angular velocities accelerate in a half period and decelerate in another half period, keeping the magnitude of the total angular velocity constant, i.e., the rotational energy keeps invariant. Correspondingly, the length of day increases gradually in one half period and decreases gradually in another half period.